Boardworks Ltd KS3 Mathematics. S1 Lines and Angles
|
|
|
- Karen Flynn
- 6 years ago
- Views:
Transcription
1 1 KS3 Mathematics S1 Lines and Angles
2 2 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons
3 3 Lines In Mathematics, a straight line is defined as having infinite length and no width. Is this possible in real life?
4 4 Labelling line segments When a line has end points we say that it has finite length. It is called a line segment. We usually label the end points with capital letters. For example, this line segment A B has end points A and B. We can call this line, line segment AB.
5 5 Labelling angles When two lines meet at a point an angle is formed. A B C An angle is a measure of the rotation of one of the line segments to the other. We label angles using capital letters. This angle can be described as ABC or ABC or B.
6 6 Conventions, definitions and derived properties A convention is an agreed way of describing a situation. For example, we use dashes on lines to show that they are the same length. A definition is a minimum set of conditions needed to describe something. For example, an equilateral triangle has three equal sides and three equal angles. A derived property follows from a definition For example, the angles in an equilateral triangle are each 60.
7 7 Convention, definition or derived property?
8 8 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons
9 9 Lines in a plane What can you say about these pairs of lines? These lines cross, or intersect. These lines do not intersect. They are parallel.
10 10 Lines in a plane A flat two-dimensional surface is called a plane. Any two straight lines in a plane either intersect once This is called the point of intersection.
11 11 Lines in a plane or they are parallel. We use arrow heads to show that lines are parallel. Parallel lines will never meet. They stay an equal distance apart. This means that they are always equidistant. Where do you see parallel lines in everyday life?
12 12 Perpendicular lines What is special about the angles at the point of intersection here? d a c b a = b = c = d Each angle is 90. We show this with a small square in each corner. Lines that intersect at right angles are called perpendicular lines.
13 13 Parallel or perpendicular?
14 14 The distance from a point to a line What is the shortest distance from a point to a line? O The shortest distance from a point to a line is always the perpendicular distance.
15 15 Drawing perpendicular lines with a set square We can draw perpendicular lines using a ruler and a set square. Draw a straight line using a ruler. Place the set square on the ruler and use the right angle to draw a line perpendicular to this line.
16 16 Drawing parallel lines with a set square We can also draw parallel lines using a ruler and a set square. Place the set square on the ruler and use it to draw a straight line perpendicular to the ruler s edge. Slide the set square along the ruler to draw a line parallel to the first.
17 17 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons
18 18 Angles Angles are measured in degrees. 90 A quarter turn measures 90. It is called a right angle. We label a right angle with a small square.
19 19 Angles Angles are measured in degrees. A half turn measures This is a straight line.
20 20 Angles Angles are measured in degrees. 270 A three-quarter turn measures 270.
21 21 Angles Angles are measured in degrees. 360 A full turn measures 360.
22 22 Intersecting lines
23 23 Vertically opposite angles When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are equal.
24 24 Angles on a straight line
25 25 Angles on a straight line Angles on a line add up to 180. a b a + b = 180 because there are 180 in a half turn.
26 26 Angles around a point
27 27 Angles around a point Angles around a point add up to 360. a b d c a + b + c + d = 360 because there are 360 in a full turn.
28 Calculating angles around a point Use geometrical reasoning to find the size of the labelled angles. a d 43 b 43 c
29 29 Complementary angles When two angles add up to 90 they are called complementary angles. a b a + b = 90 Angle a and angle b are complementary angles.
30 30 Supplementary angles When two angles add up to 180 they are called supplementary angles. a b a + b = 180 Angle a and angle b are supplementary angles.
31 31 Angles made with parallel lines When a straight line crosses two parallel lines eight angles are formed. b c a d f g e h Which angles are equal to each other?
32 32 Angles made with parallel lines
33 33 Corresponding angles There are four pairs of corresponding angles, or F-angles. b a c d f e g h d = h because Corresponding angles are equal
34 34 Corresponding angles There are four pairs of corresponding angles, or F-angles. b c a d f g e h a = e because Corresponding angles are equal
35 35 Corresponding angles There are four pairs of corresponding angles, or F-angles. b c a d f g e h c = g because Corresponding angles are equal
36 36 Corresponding angles There are four pairs of corresponding angles, or F-angles. b c a d f g e h b = f because Corresponding angles are equal
37 37 Alternate angles There are two pairs of alternate angles, or Z-angles. b c a d f g e h d = f because Alternate angles are equal
38 38 Alternate angles There are two pairs of alternate angles, or Z-angles. b c a d f g e h c = e because Alternate angles are equal
39 39 Calculating angles Calculate the size of angle a. 29º a 46º Hint: Add another line. a = 29º + 46º = 75º
40 40 Contents S1 Lines and angles S1.1 Labelling lines and angles S1.2 Parallel and perpendicular lines S1.3 Calculating angles S1.4 Angles in polygons
41 41 Angles in a triangle
42 42 Angles in a triangle c a b For any triangle, a + b + c = 180 The angles in a triangle add up to 180.
43 43 Angles in a triangle We can prove that the sum of the angles in a triangle is 180 by drawing a line parallel to one of the sides through the opposite vertex. a c b a b These angles are equal because they are alternate angles. Call this angle c. a + b + c = 180 because they lie on a straight line. The angles a, b and c in the triangle also add up to 180.
44 44 Calculating angles in a triangle Calculate the size of the missing angles in each of the following triangles a 64 b c d
45 45 Angles in an isosceles triangle In an isosceles triangle, two of the sides are equal. We indicate the equal sides by drawing dashes on them. The two angles at the bottom on the equal sides are called base angles. The two base angles are also equal. If we are told one angle in an isosceles triangle we can work out the other two.
46 46 Angles in an isosceles triangle For example, a 46 a Find the size of the other two angles. The two unknown angles are equal so call them both a. We can use the fact that the angles in a triangle add up to 180 to write an equation a + a = a = 180 2a = 92 a = 46
47 47 Polygons A polygon is a 2-D shape made when line segments enclose a region. The line segments are called sides. B A E The end points are called vertices. One of these is called a vertex. C D 2-D stands for two-dimensional. These two dimensions are length and width. A polygon has no height.
48 48 Naming polygons Polygons are named according to the number of sides they have. Number of sides Name of polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon
49 49 Interior angles in polygons The angles inside a polygon are called interior angles. b c a The sum of the interior angles of a triangle is 180.
50 50 Exterior angles in polygons When we extend the sides of a polygon outside the shape exterior angles are formed. e d f
51 51 Interior and exterior angles in a triangle Any exterior angle in a triangle is equal to the sum of the two opposite interior angles. c b ca b a = b + c We can prove this by constructing a line parallel to this side. These alternate angles are equal. These corresponding angles are equal.
52 52 Interior and exterior angles in a triangle
53 53 Calculating angles Calculate the size of the lettered angles in each of the following triangles. 33 a 116 b d c
54 54 Calculating angles Calculate the size of the lettered angles in this diagram º 38º 86 a 69 b Base angles in the isosceles triangle = (180º 104º) 2 = 76º 2 = 38º Angle a = 180º 56º 38º = 86º Angle b = 180º 73º 38º = 69º
55 55 Sum of the interior angles in a quadrilateral What is the sum of the interior angles in a quadrilateral? c d f a b e We can work this out by dividing the quadrilateral into two triangles. a + b + c = 180 and d + e + f = 180 So, (a + b + c) + (d + e + f ) = 360 The sum of the interior angles in a quadrilateral is 360.
56 56 Sum of interior angles in a polygon We already know that the sum of the interior angles in any triangle is 180. c a + b + c = 180 a b a b d c We have just shown that the sum of the interior angles in any quadrilateral is 360. a + b + c + d = 360 Do you know the sum of the interior angles for any other polygons?
57 57 Sum of the interior angles in a pentagon What is the sum of the interior angles in a pentagon? a b c e d h f g i We can work this out by using lines from one vertex to divide the pentagon into three triangles. a + b + c = 180 and d + e + f = 180 So, (a + b + c) + (d + e + f ) + (g + h + i) = 560 and g + h + i = 180 The sum of the interior angles in a pentagon is 560.
58 58 Sum of the interior angles in a polygon We ve seen that a quadrilateral can be divided into two triangles and a pentagon can be divided into three triangles. A How hexagon many triangles can be divided can a hexagon into four be divided triangles. into?
59 59 Sum of the interior angles in a polygon The number of triangles that a polygon can be divided into is always two less than the number of sides. We can say that: A polygon with n sides can be divided into (n 2) triangles. The sum of the interior angles in a triangle is 180. So, The sum of the interior angles in an n-sided polygon is (n 2) 180.
60 60 Interior angles in regular polygons A regular polygon has equal sides and equal angles. We can work out the size of the interior angles in a regular polygon as follows: Name of regular polygon Sum of the interior angles Size of each interior angle Equilateral triangle = 60 Square = = 90 Regular pentagon = = 108 Regular hexagon = = 120
61 61 Interior and exterior angles in an equilateral triangle In an equilateral triangle, Every interior angle measures 60. Every exterior angle measures The sum of the interior angles is 3 60 = 180. The sum of the exterior angles is = 360.
62 62 Interior and exterior angles in a square In a square, Every interior angle measures 90. Every exterior angle measures The sum of the interior angles is 4 90 = 360. The sum of the exterior angles is 4 90 = 360.
63 63 Interior and exterior angles in a regular pentagon In a regular pentagon, Every interior angle measures 108. Every exterior angle measures 72. The sum of the interior angles is = 540. The sum of the exterior angles is 5 72 = 360.
64 64 Interior and exterior angles in a regular hexagon In a regular hexagon, Every interior angle measures 120. Every exterior angle measures 60. The sum of the interior angles is = 720. The sum of the exterior angles is 6 60 = 360.
65 65 The sum of exterior angles in a polygon For any polygon, the sum of the interior and exterior angles at each vertex is 180. For n vertices, the sum of n interior and n exterior angles is n 180 or 180n. The sum of the interior angles is (n 2) 180. We can write this algebraically as 180(n 2) = 180n 360.
66 66 The sum of exterior angles in a polygon If the sum of both the interior and the exterior angles is 180n and the sum of the interior angles is 180n 360, the sum of the exterior angles is the difference between these two. The sum of the exterior angles = 180n (180n 360 ) = 180n 180n = 360 The sum of the exterior angles in a polygon is 360.
67 67 Take Turtle for a walk
68 68 Find the number of sides
69 69 Calculate the missing angles 50º This pattern has been made with three different shaped tiles. The length of each side is the same. What shape are the tiles? Calculate the sizes of each angle in the pattern and use this to show that the red tiles must be squares. = 50º = 40º = 130º = 140º = 140º = 150º
Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.
Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity
Contents. Lines, angles and polygons: Parallel lines and angles. Triangles. Quadrilaterals. Angles in polygons. Congruence.
Colegio Herma. Maths Bilingual Departament Isabel Martos Martínez. 2015 Contents Lines, angles and polygons: Parallel lines and angles Triangles Quadrilaterals Angles in polygons Congruence Similarity
Points, lines, angles
Points, lines, angles Point Line Line segment Parallel Lines Perpendicular lines Vertex Angle Full Turn An exact location. A point does not have any parts. A straight length that extends infinitely in
Unit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 2 WHAT YOU WILL LEARN Points, lines, planes, and
PLC Papers Created For:
PLC Papers Created For: Year 10 Topic Practice Papers: Polygons Polygons 1 Grade 4 Look at the shapes below A B C Shape A, B and C are polygons Write down the mathematical name for each of the polygons
Lines Plane A flat surface that has no thickness and extends forever.
Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that
Unit 8 Chapter 3 Properties of Angles and Triangles
Unit 8 Chapter 3 Properties of Angles and Triangles May 16 7:01 PM Types of lines 1) Parallel Lines lines that do not (and will not) cross each other are labeled using matching arrowheads are always the
Section 9.1. Points, Lines, Planes, and Angles. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 9.1 Points, Lines, Planes, and Angles What You Will Learn Points Lines Planes Angles 9.1-2 Basic Terms A point, line, and plane are three basic terms in geometry that are NOT given a formal definition,
Math 6, Unit 8 Notes: Geometric Relationships
Math 6, Unit 8 Notes: Geometric Relationships Points, Lines and Planes; Line Segments and Rays As we begin any new topic, we have to familiarize ourselves with the language and notation to be successful.
Cambridge Essentials Mathematics Core 9 GM1.1 Answers. 1 a
GM1.1 Answers 1 a b 2 Shape Name Regular Irregular Convex Concave A Decagon B Octagon C Pentagon D Quadrilateral E Heptagon F Hexagon G Quadrilateral H Triangle I Triangle J Hexagon Original Material Cambridge
Any questions about the material so far? About the exercises?
Any questions about the material so far? About the exercises? Here is a question for you. In the diagram on the board, DE is parallel to AC, DB = 4, AB = 9 and BE = 8. What is the length EC? Polygons Definitions:
Point A location in geometry. A point has no dimensions without any length, width, or depth. This is represented by a dot and is usually labelled.
Test Date: November 3, 2016 Format: Scored out of 100 points. 8 Multiple Choice (40) / 8 Short Response (60) Topics: Points, Angles, Linear Objects, and Planes Recognizing the steps and procedures for
Chapter 1-2 Points, Lines, and Planes
Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines
Geometry Reasons for Proofs Chapter 1
Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms
Describe Plane Shapes
Lesson 12.1 Describe Plane Shapes You can use math words to describe plane shapes. point an exact position or location line endpoints line segment ray a straight path that goes in two directions without
Math 7, Unit 8: Geometric Figures Notes
Math 7, Unit 8: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My guess
Convex polygon - a polygon such that no line containing a side of the polygon will contain a point in the interior of the polygon.
Chapter 7 Polygons A polygon can be described by two conditions: 1. No two segments with a common endpoint are collinear. 2. Each segment intersects exactly two other segments, but only on the endpoints.
1.6 Classifying Polygons
www.ck12.org Chapter 1. Basics of Geometry 1.6 Classifying Polygons Learning Objectives Define triangle and polygon. Classify triangles by their sides and angles. Understand the difference between convex
Review Interior Angle Sum New: Exterior Angle Sum
Review Interior Angle Sum New: Exterior Angle Sum QUIZ: Prove that the diagonal connecting the vertex angles of a kite cut the kite into two congruent triangles. 1 Interior Angle Sum Formula: Some Problems
Main Idea: classify polygons and determine which polygons can form a tessellation.
10 8: Polygons and Tesselations Main Idea: classify polygons and determine which polygons can form a tessellation. Vocabulary: polygon A simple closed figure in a plane formed by three or more line segments
a triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
Math 7, Unit 08: Geometric Figures Notes
Math 7, Unit 08: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My
Term Definition Figure
Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do
Geometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
Lesson Polygons
Lesson 4.1 - Polygons Obj.: classify polygons by their sides. classify quadrilaterals by their attributes. find the sum of the angle measures in a polygon. Decagon - A polygon with ten sides. Dodecagon
Example 1. Find the angle measure of angle b, using opposite angles.
2..1 Exploring Parallel Lines Vertically opposite angles are equal When two lines intersect, the opposite angles are equal. Supplementary angles add to 180 Two (or more) adjacent angles on the same side
Shapes and Designs - Unit Test Review Sheet
Name: Class: Date: ID: A Shapes and Designs - Unit Test Review Sheet 1. a. Suppose the measure of an angle is 25. What is the measure of its complementary angle? b. Draw the angles to show that you are
The National Strategies Secondary Mathematics exemplification: Y8, 9
Mathematics exemplification: Y8, 9 183 As outcomes, Year 8 pupils should, for example: Understand a proof that the sum of the angles of a triangle is 180 and of a quadrilateral is 360, and that the exterior
Angles in a polygon Lecture 419
Angles in a polygon Lecture 419 Formula For an n-sided polygon, the number of degrees for the sum of the internal angles is 180(n-2)º. For n=3 (triangle), it's 180. For n=4 (quadrilateral), it's 360. And
Geometry Vocabulary. Name Class
Geometry Vocabulary Name Class Definition/Description Symbol/Sketch 1 point An exact location in space. In two dimensions, an ordered pair specifies a point in a coordinate plane: (x,y) 2 line 3a line
MATH 113 Section 8.2: Two-Dimensional Figures
MATH 113 Section 8.2: Two-Dimensional Figures Prof. Jonathan Duncan Walla Walla University Winter Quarter, 2008 Outline 1 Classifying Two-Dimensional Shapes 2 Polygons Triangles Quadrilaterals 3 Other
Math Polygons
Math 310 9.2 Polygons Curve & Connected Idea The idea of a curve is something you could draw on paper without lifting your pencil. The idea of connected is that a set can t be split into two disjoint sets.
LESSON SUMMARY. Properties of Shapes
LESSON SUMMARY CXC CSEC MATHEMATICS UNIT Seven: Geometry Lesson 13 Properties of Shapes Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volume 1 and 2. (Some helpful exercises and page numbers
Unit 3: Triangles and Polygons
Unit 3: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about triangles. Objective: By the end of class, I should Example 1: Trapezoid on the coordinate plane below has the following
Angles, Polygons, Circles
Page 1 of 5 Part One Last week we learned about the angle properties of circles and used them to solve a simple puzzle. This week brings a new puzzle that will make us use our algebra a bit more. But first,
SHAPE AND STRUCTURE. Shape and Structure. An explanation of Mathematical terminology
Shape and Structure An explanation of Mathematical terminology 2005 1 POINT A dot Dots join to make lines LINE A line is 1 dimensional (length) A line is a series of points touching each other and extending
Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review
Geometry Unit 6 Properties of Quadrilaterals Classifying Polygons Review Polygon a closed plane figure with at least 3 sides that are segments -the sides do not intersect except at the vertices N-gon -
Warm-Up Exercises. 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. ANSWER 81º
Warm-Up Exercises 1. If the measures of two angles of a triangle are 19º and 80º, find the measure of the third angle. 81º 2. Solve (x 2)180 = 1980. 13 Warm-Up Exercises 3. Find the value of x. 126 EXAMPLE
Geometry Vocabulary. acute angle-an angle measuring less than 90 degrees
Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that
U4 Polygon Notes January 11, 2017 Unit 4: Polygons
Unit 4: Polygons 180 Complimentary Opposite exterior Practice Makes Perfect! Example: Example: Practice Makes Perfect! Def: Midsegment of a triangle - a segment that connects the midpoints of two sides
Geometry Ch 7 Quadrilaterals January 06, 2016
Theorem 17: Equal corresponding angles mean that lines are parallel. Corollary 1: Equal alternate interior angles mean that lines are parallel. Corollary 2: Supplementary interior angles on the same side
Reporting Category 3. Geometry and Measurement BINGO
Reporting Category 3 Geometry and Measurement BINGO names an exact location in space, named by a capital letter Has NO width, length, or depth. 2 a straight path with 2 endpoints, has a definite beginning
6.7 Regular Polygons
6.7 Regular Polygons Dec 13 3:08 PM 1 Recall, what is a polygon? A union of segments in the same plane such that each segment intersects two others, one at each of its endpoints Dec 13 3:13 PM 2 Define
Chapter 8. Properties of Triangles and Quadrilaterals. 02/2017 LSowatsky
Chapter 8 Properties of Triangles and Quadrilaterals 02/2017 LSowatsky 1 8-1A: Points, Lines, and Planes I can Identify and label basic geometric figures. LSowatsky 2 Vocabulary: Point: a point has no
1. Write three things you already know about angles. Share your work with a classmate. Does your classmate understand what you wrote?
LESSON : PAPER FOLDING. Write three things you already know about angles. Share your work with a classmate. Does your classmate understand what you wrote? 2. Write your wonderings about angles. Share your
Right Angle Triangle. Square. Opposite sides are parallel
Triangles 3 sides ngles add up to 18⁰ Right ngle Triangle Equilateral Triangle ll sides are the same length ll angles are 6⁰ Scalene Triangle ll sides are different lengths ll angles are different Isosceles
ame Date Class Practice A 11. What is another name for a regular quadrilateral with four right angles?
ame Date Class Practice A Polygons Name each polygon. 1. 2. 3. 4. 5. 6. Tell whether each polygon appears to be regular or not regular. 7. 8. 9. 10. What is another name for a regular triangle? 11. What
Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?
Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each
15. First make a parallelogram by rotating the original triangle. Then tile with the Parallelogram.
Shapes and Designs: Homework Examples from ACE Investigation 1: Question 15 Investigation 2: Questions 4, 20, 24 Investigation 3: Questions 2, 12 Investigation 4: Questions 9 12, 22. ACE Question ACE Investigation
Geometry Practice. 1. Angles located next to one another sharing a common side are called angles.
Geometry Practice Name 1. Angles located next to one another sharing a common side are called angles. 2. Planes that meet to form right angles are called planes. 3. Lines that cross are called lines. 4.
Math-in-CTE Lesson Plan Template
Lesson Development Math-in-CTE Lesson Plan Template Lesson Title: Basic Geometric Concepts Lesson # Author(s): Phone Number(s): E-mail Address(es): Juan Carlos Martínez jcmartinez@dadeschoolsnet Bergman
ACT Math test Plane Geometry Review
Plane geometry problems account for 14 questions on the ACT Math Test that s almost a quarter of the questions on the Subject Test. If you ve taken high school geometry, you ve probably covered all of
UNIT 6: Connecting Algebra & Geometry through Coordinates
TASK: Vocabulary UNIT 6: Connecting Algebra & Geometry through Coordinates Learning Target: I can identify, define and sketch all the vocabulary for UNIT 6. Materials Needed: 4 pieces of white computer
Introduction to Geometry
Introduction to Geometry Objective A: Problems involving lines and angles Three basic concepts of Geometry are: Points are a single place represented by a dot A Lines are a collection of points that continue
ACT SparkNotes Test Prep: Plane Geometry
ACT SparkNotes Test Prep: Plane Geometry Plane Geometry Plane geometry problems account for 14 questions on the ACT Math Test that s almost a quarter of the questions on the Subject Test If you ve taken
Polygons. Name each polygon Find the sum of the angle measures in each figure
Practice A Polygons Name each polygon. 1. 2. 3. Find the sum of the angle measures in each figure. 4. 5. 6. 7. 8. 9. Find the angle measures in each regular polygon. 10. 11. 12. 13. 14. 15. Give all the
Mrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Reflectional Symmetry
A triangle ( ) is the union of three segments determined by three noncollinear points.
Chapter 6 Triangles & Polygons A triangle ( ) is the union of three segments determined by three noncollinear points. C Each of the three points, A, B and C is a vertex of the triangle. A B AB, BC, and
Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?
Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each
MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary. Section 11-1: Basic Notions
MAT104: Fundamentals of Mathematics II Introductory Geometry Terminology Summary Section 11-1: Basic Notions Undefined Terms: Point; Line; Plane Collinear Points: points that lie on the same line Between[-ness]:
Special Lines and Constructions of Regular Polygons
Special Lines and Constructions of Regular Polygons A regular polygon with a center A is made up of congruent isosceles triangles with a principal angle A. The red line in the regular pentagon below is
An angle that has a measure less than a right angle.
Unit 1 Study Strategies: Two-Dimensional Figures Lesson Vocab Word Definition Example Formed by two rays or line segments that have the same 1 Angle endpoint. The shared endpoint is called the vertex.
Yimin Math Centre. 6.1 Properties of geometrical figures Recognising plane shapes... 1
Yimin Math Centre Student Name: Grade: Date: Score: Table of Contents 6 Year 7 Term 3 Week 6 Homework 1 6.1 Properties of geometrical figures............................ 1 6.1.1 Recognising plane shapes...........................
STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY. 3 rd Nine Weeks,
STANDARDS OF LEARNING CONTENT REVIEW NOTES HONORS GEOMETRY 3 rd Nine Weeks, 2016-2017 1 OVERVIEW Geometry Content Review Notes are designed by the High School Mathematics Steering Committee as a resource
Euclid s Muse Directions
Euclid s Muse Directions First: Draw and label three columns on your chart paper as shown below. Name Picture Definition Tape your cards to the chart paper (3 per page) in the appropriate columns. Name
CARDSTOCK MODELING Math Manipulative Kit. Student Activity Book
CARDSTOCK MODELING Math Manipulative Kit Student Activity Book TABLE OF CONTENTS Activity Sheet for L.E. #1 - Getting Started...3-4 Activity Sheet for L.E. #2 - Squares and Cubes (Hexahedrons)...5-8 Activity
GCSE GRADE D. Equivalent fractions, decimals & percentages. Percentage to decimal to fraction. Fraction to decimal to percentage
Equivalent fractions, decimals & percentages Percentage to decimal to fraction Fraction to decimal to percentage Decimal to percentage to fraction Increase/Decrease by a percentage Divide a quantity into
Secondary Math II Honors. Unit 4 Notes. Polygons. Name: Per:
Secondary Math II Honors Unit 4 Notes Polygons Name: Per: Day 1: Interior and Exterior Angles of a Polygon Unit 4 Notes / Secondary 2 Honors Vocabulary: Polygon: Regular Polygon: Example(s): Discover the
Explore 2 Exploring Interior Angles in Polygons
Explore 2 Exploring Interior Angles in Polygons To determine the sum of the interior angles for any polygon, you can use what you know about the Triangle Sum Theorem by considering how many triangles there
7) Are HD and HA the same line?
Review for Exam 2 Math 123 SHORT ANSWER. You must show all work to receive full credit. Refer to the figure to classify the statement as true or false. 7) Are HD and HA the same line? Yes 8) What is the
12.4 Rotations. Learning Objectives. Review Queue. Defining Rotations Rotations
12.4. Rotations www.ck12.org 12.4 Rotations Learning Objectives Find the image of a figure in a rotation in a coordinate plane. Recognize that a rotation is an isometry. Review Queue 1. Reflect XY Z with
Number and Operations - Fractions
NF.1.3c Number and Operations - Fractions NF.1.3 NF.1.2b NF.1.2a Understand Fractions February 3 - February 20 NF.1.2 NF.1.1 Math! Lessons Develop understanding of fractions as numbers. Understand a fraction
If lines m and n are parallel, we write. Transversal: A line that INTERSECTS two or more lines at 2
Unit 4 Lesson 1: Parallel Lines and Transversals Name: COMPLEMENTARY are angles to add up to 90 SUPPLEMENTARY are angles to add up to 180 These angles are also known as a LINEAR PAIR because they form
Geometry Foundations Planning Document
Geometry Foundations Planning Document Unit 1: Chromatic Numbers Unit Overview A variety of topics allows students to begin the year successfully, review basic fundamentals, develop cooperative learning
Oral and mental starter
Lesson 8 Objectives Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes (Y7) Vocabulary parallel, perpendicular, transversal, intersecting, vertically opposite,
Unit 1, Lesson 1: Moving in the Plane
Unit 1, Lesson 1: Moving in the Plane Let s describe ways figures can move in the plane. 1.1: Which One Doesn t Belong: Diagrams Which one doesn t belong? 1.2: Triangle Square Dance m.openup.org/1/8-1-1-2
Park Forest Math Team. Meet #3. Self-study Packet
Park Forest Math Team Meet #3 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Properties of Polygons, Pythagorean Theorem 3.
Unit 3 Geometry. Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D
Unit 3 Geometry Chapter 7 Geometric Relationships Chapter 8 Measurement Relationships Chapter 9 Optimizing Measurements MPM1D Chapter 7 Outline Section Subject Homework Notes Lesson and Homework Complete
Unit 2: Triangles and Polygons
Unit 2: Triangles and Polygons Background for Standard G.CO.9: Prove theorems about lines and angles. Objective: By the end of class, I should Using the diagram below, answer the following questions. Line
MPM1D Page 1 of 6. length, width, thickness, area, volume, flatness, infinite extent, contains infinite number of points. A part of a with endpoints.
MPM1D Page 1 of 6 Unit 5 Lesson 1 (Review) Date: Review of Polygons Activity 1: Watch: http://www.mathsisfun.com/geometry/dimensions.html OBJECT Point # of DIMENSIONS CHARACTERISTICS location, length,
Pre-Algebra, Unit 10: Measurement, Area, and Volume Notes
Pre-Algebra, Unit 0: Measurement, Area, and Volume Notes Triangles, Quadrilaterals, and Polygons Objective: (4.6) The student will classify polygons. Take this opportunity to review vocabulary and previous
Angle Unit Definitions
ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers
The Ultimate Maths Vocabulary List
The Ultimate Maths Vocabulary List The 96 Words Every Pupil Needs to Know by the End of Year 6 KS1 & KS2 How to Use This Resource An essential building block in pupil s understanding of maths is their
Tessellations: Wallpapers, Escher & Soccer Balls. Robert Campbell
Tessellations: Wallpapers, Escher & Soccer Balls Robert Campbell Tessellation Examples What Is What is a Tessellation? A Tessellation (or tiling) is a pattern made by copies of one or
Chapter Review. In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning.
In the figure shown, m n and r is a transversal. If m 4 = 112, find the measure of each angle. Explain your reasoning. 1. 6 Since 4 and 6 are alternate interior angles, they are congruent. So, m 6 = 112.
Geometry End of Course Review
1 Area of a rectangle is equal to base x height. For a triangle Area = ½ (bh) or one half base x height. The height must be the perpendicular distance from the base to the tallest part. The area of a circle
Quarter 1 Study Guide Honors Geometry
Name: Date: Period: Topic 1: Vocabulary Quarter 1 Study Guide Honors Geometry Date of Quarterly Assessment: Define geometric terms in my own words. 1. For each of the following terms, choose one of the
Math 6, Unit 8 Notes: Geometric Relationships
Math 6, Unit 8 Notes: Geometric Relationships Points, Lines and Planes; Line Segments and Rays As we begin any new topic, we have to familiarize ourselves with the language and notation to be successful.
Answer Key. 1.1 The Three Dimensions. Chapter 1 Basics of Geometry. CK-12 Geometry Honors Concepts 1. Answers
1.1 The Three Dimensions 1. Possible answer: You need only one number to describe the location of a point on a line. You need two numbers to describe the location of a point on a plane. 2. vary. Possible
pine cone Ratio = 13:8 or 8:5
Chapter 10: Introducing Geometry 10.1 Basic Ideas of Geometry Geometry is everywhere o Road signs o Carpentry o Architecture o Interior design o Advertising o Art o Science Understanding and appreciating
Polygon. Note: Each segment is called a side. Each endpoint is called a vertex.
Polygons Polygon A closed plane figure formed by 3 or more segments. Each segment intersects exactly 2 other segments at their endpoints. No 2 segments with a common endpoint are collinear. Note: Each
14. How many sides does a regular polygon have, if the measure of an interior angle is 60?
State whether the figure is a polygon; if it is a polygon, state whether the polygon is convex or concave. HINT: No curves, no gaps, and no overlaps! 1. 2. 3. 4. Find the indicated measures of the polygon.
Closed shapes with straight sides
41 Unit 6 and 7 Properties of 2D shapes Activity 1 Closed shapes with straight sides (polygons). Let s revise the 2D shapes you learnt about in Grade 5 Closed shapes with straight sides triangle quadrilateral
Mrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Refectional Symmetry Definition:
Section 1-1 Points, Lines, and Planes
Section 1-1 Points, Lines, and Planes I CAN. Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in space. Undefined Term- Words, usually
Number/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative
6 Polygons and. Quadrilaterals CHAPTER. Chapter Outline.
www.ck12.org CHAPTER 6 Polygons and Quadrilaterals Chapter Outline 6.1 ANGLES IN POLYGONS 6.2 PROPERTIES OF PARALLELOGRAMS 6.3 PROVING QUADRILATERALS ARE PARALLELOGRAMS 6.4 RECTANGLES, RHOMBUSES AND SQUARES
Grade 8 Math WORKBOOK UNIT 1 : POLYGONS. Are these polygons? Justify your answer by explaining WHY or WHY NOT???
Grade 8 Math WORKBOOK UNIT 1 : POLYGONS Are these polygons? Justify your answer by explaining WHY or WHY NOT??? a) b) c) Yes or No Why/Why not? Yes or No Why/Why not? Yes or No Why/Why not? a) What is
Chapter 7 Geometric Relationships. Practice Worksheets MPM1D
Chapter 7 Geometric Relationships Practice Worksheets MPM1D Chapter 7 Geometric Relationships Intro Worksheet MPM1D Jensen Part 1: Classify Triangles 1. Classify each triangle according to its side lengths.