7-4 Applying Properties of Similar Triangles 7-4. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
|
|
|
- Conrad Willis
- 5 years ago
- Views:
Transcription
1 7-4 Applying Properties of Similar Triangles Warm Up Lesson Presentation Lesson Quiz Geometry
2 Warm Up Solve each proportion. 1. AB = QR = x = y = 8
3 Objectives Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
4 Artists use mathematical techniques to make twodimensional paintings appear three-dimensional. The invention of perspective was based on the observation that far away objects look smaller and closer objects look larger. Mathematical theorems like the Triangle Proportionality Theorem are important in making perspective drawings.
5
6 Example 1: Finding the Length of a Segment Find US. It is given that, so by the Triangle Proportionality Theorem. US(10) = 56 Substitute 14 for RU, 4 for VT, and 10 for RV. Cross Products Prop. Divide both sides by 10.
7 Find PN. Check It Out! Example 1 Use the Triangle Proportionality Theorem. Substitute in the given values. 2PN = 15 Cross Products Prop. PN = 7.5 Divide both sides by 2.
8
9 Example 2: Verifying Segments are Parallel Verify that. Since, by the Converse of the Triangle Proportionality Theorem.
10 Check It Out! Example 2 AC = 36 cm, and BC = 27 cm. Verify that. Since, by the Converse of the Triangle Proportionality Theorem.
11
12 Example 3: Art Application Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.
13 Example 3 Continued Given 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 2.6 for BC. 4.5(LM) = 4.9(2.6) LM 2.8 in. Cross Products Prop. Divide both sides by 4.5.
14 Example 3 Continued 2-Trans. Proportionality Corollary Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD. 4.5(MN) = 4.9(4.1) Cross Products Prop. MN 4.5 in. Divide both sides by 4.5.
15 Check It Out! Example 3 Use the diagram to find LM and MN to the nearest tenth.
16 Check It Out! Example 3 Continued Given 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 1.4 for BC. 2.4(LM) = 1.4(2.6) LM 1.5 cm Cross Products Prop. Divide both sides by 2.4.
17 Check It Out! Example 3 Continued 2-Trans. Proportionality Corollary Substitute 2.6 for KL, 2.4 for AB, and 2.2 for CD. 2.4(MN) = 2.2(2.6) Cross Products Prop. MN 2.4 cm Divide both sides by 2.4.
18 The previous theorems and corollary lead to the following conclusion.
19 Example 4: Using the Triangle Angle Bisector Theorem Find PS and SR. by the Bisector Theorem. Substitute the given values. 40(x 2) = 32(x + 5) 40x 80 = 32x Cross Products Property Distributive Property
20 Example 4 Continued 40x 80 = 32x x = 240 x = 30 Simplify. Divide both sides by 8. Substitute 30 for x. PS = x 2 SR = x + 5 = 30 2 = 28 = = 35
21 Find AC and DC. Check It Out! Example 4 by the Bisector Theorem. Substitute in given values. 4y = 4.5y 9 0.5y = 9 Cross Products Theorem Simplify. y = 18 Divide both sides by 0.5. So DC = 9 and AC = 16.
22 Lesson Quiz: Part I Find the length of each segment SR = 25, ST = 15
23 Lesson Quiz: Part II 3. Verify that BE and CD are parallel. Since, by the Converse of the Proportionality Thm.
4-8 Similar Figures and Proportions. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes
Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Warm Up Find the cross products, and then tell whether the ratios are equal. 1. 16, 40 6 15 2. 3. 3 8, 18 46 8, 24 9 27 4. 28, 42 12 18 240
Pre-AP Geometry 7-1 Study Guide: Ratios in Similar Polygons (pp ) Page! 1 of! 9
Page! 1 of! 9 Attendance Problems. 1. If! VQRS VZYX, identify the pairs of congruent angles and the pairs of congruent sides. Solve each proportion. 2 2.! 3.! x 3 = 8 3x 3 x 6 42 = 2x 14 77 I can identify
6-3 Conditions for Parallelograms
6-3 Conditions for Parallelograms Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and
If- = then ai = L-c b d
I^otes: Ratios and Proportions the comparison of two numbers using C^i'i/t'S/'o^, written'^a to b", a:b, or ^ (b7^ 0) Proportion an equation that states two rdho are equal; ex: 7 = (b 0, d ^ 0) b a Cross
Geo: Unit 7 Relationships with Triangles Unit 7 Relationships with Triangles
Unit 7 Relationships with Triangles Target 7.1: Use the midsegment to determine unknown information of triangles Target 7.2: Apply perpendicular bisectors and angle bisectors to find unknowns 7.2a Perpendicular
Chapter 2 Diagnostic Test
Chapter Diagnostic Test STUDENT BOOK PAGES 68 7. Calculate each unknown side length. Round to two decimal places, if necessary. a) b). Solve each equation. Round to one decimal place, if necessary. a)
Geometry SIA #2. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.
Class: Date: Geometry SIA #2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. a. 4 b. 8 c. 6.6 d. 6 2. Find the length of the midsegment.
Warm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p.
Warm-Up Up Exercises Use this diagram for Exercises 1 4. 1. If PR = 12 and m R = 19, find p. ANSWER 11.3 2. If m P = 58 and r = 5, find p. ANSWER 8.0 Warm-Up Up Exercises Use this diagram for Exercises
Ratios in Similar Polygons
Warm Up 1. If QRS ZYX, identify the pairs of congruent angles and the pairs of congruent sides. Q Z; R Y; S X; QR ZY; RS YX; QS ZX Solve each proportion. 2. 3. x = 9 x = 18 Objectives EQ: How do you use
Name Date Class. 6. In JKLM, what is the value of m K? A 15 B 57 A RS QT C QR ST
Name Date Class CHAPTER 6 Chapter Review #1 Form B Circle the best answer. 1. Which best describes the figure? 6. In JKLM, what is the value of m K? A regular convex heptagon B irregular convex heptagon
Section 4-1 Congruent Figures. Objectives: recognize congruent figures and their corresponding parts
Section 4-1 Congruent Figures Objectives: recognize congruent figures and their corresponding parts Congruent Polygons Congruent Polygons have congruent corresponding parts Congruent sides Congruent Angles
7-5 Parts of Similar Triangles. Find x.
Find x. 1. By AA Similarity, the given two triangles are similar. Additionally, we see the segments marked x and 10 are medians because they intersect the opposite side at its midpoint. Theorem 7.10 states
Congruent Triangles Triangles. Warm Up Lesson Presentation Lesson Quiz. Holt Geometry. McDougal Geometry
Triangles Warm Up Lesson Presentation Lesson Quiz Holt Geometry McDougal Geometry Warm Up 1. Name all sides and angles of FGH. FG, GH, FH, F, G, H 2. What is true about K and L? Why? ;Third s Thm. 3. What
FGCU Invitational Geometry Individual 2014
All numbers are assumed to be real. Diagrams are not drawn to scale. For all questions, NOTA represents none of the above answers is correct. For problems 1 and 2, refer to the figure in which AC BC and
Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.
Name Homework Packet 7.6 7.7 LESSON 7.6 For use with pages 473-480 AND LESSON 7.7 For use with pages 483 489 Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal.
**If all seven assignments are completed by the day the Mod 12 test is given you will receive 3 extra points on the test. **
Geometry Mod 11 &12 Similarity Section 6.1: I can solve problems by writing and using rates and ratios. I can solve problems by writing and solving proportions. I can use the geometric mean to solve problems.
Unit 8: Similarity. Part 1 of 2: Intro to Similarity and Special Proportions
Name: Geometry Period Unit 8: Similarity Part 1 of 2: Intro to Similarity and Special Proportions In this unit you must bring the following materials with you to class every day: Please note: Calculator
UNIT 1 SIMILARITY, CONGRUENCE, AND PROOFS Lesson 7: Proving Similarity Instruction
Prerequisite Skills This lesson requires the use of the following skills: identifying similar triangles using similarity statements to find unknown lengths and measures of similar triangles using the distance
7-5 Parts of Similar Triangles. Find x.
Find x. 1. By AA Similarity, the given two triangles are similar. Additionally, we see the segments marked x and 10 are medians because they intersect the opposite side at its midpoint. Theorem 7.10 states
Modeling with Geometry
Modeling with Geometry 6.3 Parallelograms https://mathbitsnotebook.com/geometry/quadrilaterals/qdparallelograms.html Properties of Parallelograms Sides A parallelogram is a quadrilateral with both pairs
Unit 5 Applying Similarity of Triangles
Unit 5 Applying Similarity of Triangles Lesson 1: Proof of the Triangle Side Splitter Theorem Opening Exercise We are going to construct a proof designed to demonstrate the following theorem: A line segment
Geometry Notes Chapter 4: Triangles
Geometry Notes Chapter 4: Triangles Name Date Assignment Questions I have Day 1 Section 4.1: Triangle Sum, Exterior Angles, and Classifying Triangles Day 2 Assign: Finish Ch. 3 Review Sheet, WS 4.1 Section
no triangle can have more than one right angle or obtuse angle.
Congruence Theorems in Action Isosceles Triangle Theorems.3 Learning Goals In this lesson, you will: Prove the Isosceles Triangle Base Theorem. Prove the Isosceles Triangle Vertex Angle Theorem. Prove
When two polygons have the same shape and only differ in size, we say they are similar polygons.
Chapter 10 Similar Polygons When two polygons have the same shape and only differ in size, we say they are similar polygons. These two pentagons are similar. More formally, two polygons are similar if
MST Topics in the History of Mathematics
MST Topics in the History of Mathematics Paul Yiu Department of Mathematics Florida Atlantic University Summer 2011 3B: Euclid s Book VI (Similar triangles) Euclide VI.1,2 VI.1. Triangles and parallelograms
When two polygons have the same shape and only differ in size, we say they are similar polygons.
Chapter 7 Similar Polygons When two polygons have the same shape and only differ in size, we say they are similar polygons. These two pentagons are similar. More formally, two polygons are similar if and
Chapters 7 & 8. Parallel and Perpendicular Lines/Triangles and Transformations
Chapters 7 & 8 Parallel and Perpendicular Lines/Triangles and Transformations 7-2B Lines I can identify relationships of angles formed by two parallel lines cut by a transversal. 8.G.5 Symbolic Representations
8.1 Day 1 Warmup. Solve each equation. 1. 4x + 5x + 6x = (x 5) 2 = 81. in simplest form. 3. Write 16
8.1 Day 1 Warmup Solve each equation. 1. 4x + 5x + 6x = 180 2. (x 5) 2 = 81 3. Write 16 24 in simplest form. 4. If QRS ZYX, identify the pairs of congruent angles and the pairs of congruent sides. February
4-7 Triangle Congruence: CPCTC
4-7 Triangle Congruence: CPCTC Warm Up Lesson Presentation Lesson Quiz Holt Geometry McDougal Geometry Warm Up 1. If ABC DEF, then A? and BC?. D EF 2. What is the distance between (3, 4) and ( 1, 5)? 17
Geometry Semester 1 Final Review Part 1 (Units 1 3)
Name: Date: Block: Geometry Semester 1 Final Review Part 1 (Units 1 3) Unit 1 (Holt Sections 1-1 1-5) 1. Draw and label each of the following. a) a line containing points R and S. b) a ray with endpoint
10-2. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry
Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Find the unknown side lengths in each special right triangle. 1. a 30-60 -90 triangle with hypotenuse 2 ft 2. a 45-45 -90 triangle with leg length
Get Ready. Solving Equations 1. Solve each equation. a) 4x + 3 = 11 b) 8y 5 = 6y + 7
Get Ready BLM... Solving Equations. Solve each equation. a) 4x + = 8y 5 = 6y + 7 c) z+ = z+ 5 d) d = 5 5 4. Write each equation in the form y = mx + b. a) x y + = 0 5x + y 7 = 0 c) x + 6y 8 = 0 d) 5 0
6-1 Properties and Attributes of Polygons
6-1 Properties and Attributes of Polygons Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. A? is a three-sided polygon. triangle 2. A? is a four-sided polygon. quadrilateral Evaluate each expression
Review of Sine, Cosine, and Tangent for Right Triangle
Review of Sine, Cosine, and Tangent for Right Triangle In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C.
Similarity Review day 2
Similarity Review day 2 DD, 2.5 ( ΔADB ) A D B Center (, ) Scale Factor = C' C 4 A' 2 A B B' 5 The line y = ½ x 2 is dilated by a scale factor of 2 and centered at the origin. Which equation represents
Reteach. Congruence and Transformations
Congruence and Transformations TYPES OF TRANSFORMATIONS (centered at (0, 0)) Translation (slide): (x, y) (x a, y b) Reflection y-axis: (x, y) ( x, y) x-axis: (x, y) (x, y) Rotation 90 clockwise: (x, y)
Geometry - Chapter 12 Test SAMPLE
Class: Date: Geometry - Chapter 12 Test SAMPLE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the value of x. If necessary, round your answer to
Geometry. Practice End-of-Course Exam #3. Name Teacher. Per
Geometry Practice End-of-Course Exam #3 Name Teacher Per 1 Look at the pair of triangles. A B C D Which statement is true? Ο A. The triangles are congruent. Ο B. The triangles are similar but not congruent.
GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET
Name Date Class GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET For 1 2, use the graph. 6. State the converse of the statement. Then determine whether the converse is true. Explain. If two angles are vertical
Name Class Date. Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x?
12-1 Practice Tangent Lines Lines that appear to be tangent are tangent. O is the center of each circle. What is the value of x? 1. To start, identify the type of geometric figure formed by the tangent
Reteach. Understanding Points, Lines, and Planes. P point P
Name Date Class 1-1 Understanding Points, Lines, and Planes A point has no size. It is named using a capital letter. All the figures below contain points. line Figure Characteristics Diagram Words and
of Triangles Warm Up Lesson Presentation Lesson Quiz Holt McDougal Geometry
5-3 Medians Medians and and 6-3 Altitudes Altitudes of Triangles of Triangles Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up 1. What is the name of the point where the angle bisectors of a triangle
Similar Figures and Proportions
Practice A Similar Figures and Proportions Identify the corresponding sides. 1. AB corresponds to. 2. BC corresponds to. 3. AC corresponds to. Identify the corresponding sides. Then use ratios to determine
5-2 Bisectors in Triangles
5-2 Bisectors in Triangles Warm Up Lesson Presentation Lesson Quiz Geometry Objectives Prove and apply properties of perpendicular bisectors of a triangle. Prove and apply properties of angle bisectors
7.2 Similar Polygons. Geometry Mr. Peebles Spring 2013
7.2 Similar Polygons Geometry Mr. Peebles Spring 2013 Daily Learning Target (DLT) Monday February 25, 2013 I can understand, apply, and remember to identify similar polygons in real-life problems. Geometry
Lesson 10.1 Parallel and Perpendicular
Lesson 10.1 Parallel and Perpendicular 1. Find the slope of each line. a. y 4x 7 b. y 2x 7 0 c. 3x y 4 d. 2x 3y 11 e. y 4 3 (x 1) 5 f. 1 3 x 3 4 y 1 2 0 g. 1.2x 4.8y 7.3 h. y x i. y 2 x 2. Give the slope
Geometry: Chapter 7 Review: ANSWER KEY This answer key is incomplete as it does not show work. It is only meant to use to confirm your final results.
Geometry: Chapter 7 Review: ANSWER KEY This answer key is incomplete as it does not show work. It is only meant to use to confirm your final results. 1) Ratios : 7.1 A. Students should know what a ratio
Mathematics Success Grade 8
Mathematics Success Grade 8 S19 Warm Up Directions: Answer Questions 1 and 2 about ratios and proportionality. 1. Determine whether the ratios 9 and 8 12 your answer. form a proportion and explain 2. Determine
Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12)
Geometry Fundamentals Midterm Exam Review Name: (Chapter 1, 2, 3, 4, 7, 12) Date: Mod: Use the figure at the right for #1-4 1. What is another name for plane P? A. plane AE B. plane A C. plane BAD D. plane
Class IX Chapter 11 Constructions Maths
1 Class IX Chapter 11 Constructions Maths 1: Exercise 11.1 Question Construct an angle of 90 at the initial point of a given ray and justify the construction. Answer: The below given steps will be followed
Name. Geometry Honors. Unit 1 Coordinate Geometry. Practice Packet
Name Geometry Honors Unit 1 Coordinate Geometry Practice Packet 1 Slope, // Lines and Lines 1. Determine whether the lines with equations y x 1 and 1 y x 5 are parallel, perpendicular or neither. Explain
Unit 5b/Chapter 6: Similarity Name: Block:
Unit 5b/hapter 6: Similarity Name: lock: 1 2 3 4 5 6 7 8 SOL G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar, using algebraic and coordinate
Practice A. Solving Right Triangles. sin. cos A 5. tan 2
Name Date Class Solving Right Triangles In Exercises 1 3, fill in the blanks to complete the description of the inverse trigonometric ratios. 1. If sin A = x, then sin 1 x =. 2. If cos A =, then cos 1
Conditions for Parallelograms
Warm Up Justify each statement. 1. 2. Reflex Prop. of Conv. of Alt. Int. s Thm. Evaluate each expression for x = 12 and y = 8.5. 3. 2x + 7 4. 16x 9 31 183 5. (8y + 5) 73 Essential Question Unit 2D Day
Chapter 11 Areas of Polygons and Circles
Section 11-1: Areas of Parallelograms and Triangles SOL: G.14 The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, and
Pearson Foundations and Pre-calculus Mathematics 10
Cumulative Review Chapters and (pages 0-) Chapter. a) Since yd. = ft., to convert feet to yards, divide by. 70 70 ft. yd. 70 ft. yd. 70 ft. yd. ft. b) The perimeter of the pen is greater than yd., so Andrea
Chapter 6. Similarity
Chapter 6 Similarity 6.1 Use Similar Polygons Objective: Use proportions to identify similar polygons. Essential Question: If two figures are similar, how do you find the length of a missing side? Two
REVIEW Geometry B Chapter 7 (8.1, 9.5)
Class: Date: REVIEW Geometry B Chapter 7 (8.1, 9.5) Multiple Choice Identify the choice that best completes the statement or answers the question. 1. a..f b..g c..h d..i 2. Figure TQRS BCDE. Name a pair
Lesson. Warm Up flowchart proof. 2. False 3. D. Lesson Practice 48. a. assume m X m Y. b. AB is not perpendicular to CB.
Warm Up 1. flowchart proof 2. False 3. D Lesson Practice a. assume m X m Y b. AB is not perpendicular to CB. c. An isosceles triangle has no sides of equal length. d. Assume that a triangle has more than
Solv S ing olv ing ight ight riang les iangles 8-3 Solving Right Triangles Warm Up Use ABC for Exercises If a = 8 and b = 5, find c
Warm Up Lesson Presentation Lesson Quiz Warm Up Use ABC for Exercises 1 3. 1. If a = 8 and b = 5, find c. 2. If a = 60 and c = 61, find b. 11 3. If b = 6 and c = 10, find sin B. 0.6 Find AB. 4. A(8, 10),
Name Date Class Period
Name Date Class Period Activity B 4.6 Comparing Congruent Triangles MATERIALS metric ruler protractor QUESTION EXPLORE 1 If two triangles are congruent what do you know about the corresponding parts of
Geometry HR Date: 2/13/2013 ID Check 2nd Objective: SWBAT identify and use perpendicular and angle bisectors in triangles.
Geometry HR Date: 2/13/2013 ID Check 2nd Objective: SWBAT identify and use perpendicular and angle bisectors in triangles. Bell Ringer: 5 minute check 4.6/4.7 10 minutes HW Requests: Quadratics WS 2 nd
8.6. Write and Graph Exponential Decay Functions. Warm Up Lesson Presentation Lesson Quiz
8.6 Write and Graph Exponential Decay Functions Warm Up Lesson Presentation Lesson Quiz 8.6 Warm-Up. Evaluate. 3 ANSWER 8. Evaluate. 4 ANSWER 6 3. The table shows how much money Tess owes after w weeks.
Chapter 8. Properties of Quadrilaterals
Chapter 8 Properties of Quadrilaterals 8.1 Properties of Parallelograms Objective: To use the properties of parallelograms Parallelogram Theorem Description Picture Theorem 8.1 The opposite sides of a
Lesson 3.6 Overlapping Triangles
Lesson 3.6 Overlapping Triangles Getting Ready: Each division in the given triangle is 1 unit long. Hence, the side of the largest triangle is 4- unit long. Figure 3.6.1. Something to think about How many
1-1. Points, Lines, and Planes. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Points, Lines, and Planes What You ll Learn Scan the text in Lesson 1-1. Write two facts you learned about points, lines, and planes as you scanned the text. 1. Active Vocabulary 2. New Vocabulary
Math 2 Unit 2 Notes: DAY 1 Review Properties & Algebra Proofs
Math 2 Unit 2 Notes: DAY 1 Review Properties & Algebra Proofs Warm-up Addition Property of equality (add prop =) If Then a = b If 5x-7 = 23 Then If AB = CD Then AB+GH = Subtraction Property of equality
Unit 3 Similarity Figures and Dilations
Unit 3 Similarity Figures and Dilations Date Target Assignment Done! M 9-25 3.1 3.1 Worksheet T 9-26 3.2 3.2 Worksheet W 9-27 3.1-3.2 3.1-3.2 Review Worksheet R 9-28 Quiz Quiz 3.1-3.2 F 9-29 3.3a 3.3a
8 Quadrilaterals. Before
8 Quadrilaterals 8. Find Angle Measures in Polygons 8. Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 8.5 Use Properties
10-1 Circles & Circumference
10-1 Circles & Circumference Radius- Circle- Formula- Chord- Diameter- Circumference- Formula- Formula- Two circles are congruent if and only if they have congruent radii All circles are similar Concentric
Geometry 5-1 Bisector of Triangles- Live lesson
Geometry 5-1 Bisector of Triangles- Live lesson Draw a Line Segment Bisector: Draw an Angle Bisectors: Perpendicular Bisector A perpendicular bisector is a line, segment, or ray that is perpendicular to
Chapter 6: Similarity
Name: Chapter 6: Similarity Guided Notes Geometry Fall Semester CH. 6 Guided Notes, page 2 6.1 Ratios, Proportions, and the Geometric Mean Term Definition Example ratio of a to b equivalent ratios proportion
CONSTRUCTIONS Introduction Division of a Line Segment
216 MATHEMATICS CONSTRUCTIONS 11 111 Introduction In Class IX, you have done certain constructions using a straight edge (ruler) and a compass, eg, bisecting an angle, drawing the perpendicular bisector
Similar Polygons. These rectangles are not similar. In the investigation, you will explore what makes polygons similar.
CONDENSED LESSON 11.1 Similar Polygons In this lesson, you Learn what it means for two figures to be similar Use the definition of similarity to find missing measures in similar polygons Explore dilations
Geometry. Congruent Triangles. Unit 4. Name:
Geometry Unit 4 Congruent Triangles Name: 1 Geometry Chapter 4 Congruent Triangles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** 1. (4-1)
Date Target Assignment Done! W Review Worksheet. F 9-30 Project Cartoon Enlargement Project. T a 3.
Unit 3 Similar Figures and Dilations Target 1: Use proportions to identify lengths of corresponding parts in similar figures. Target 2: Perform and identify dilations. Target 3: Use sclae factor and similarity
You can use theorems about the interior and exterior angles of convex polygons to solve problems.
8 Big Idea CATER SUMMARY BI IDEAS Using Angle Relationships in olygons You can use theorems about the interior and exterior angles of convex polygons to solve problems. or Your Notebook olygon Interior
General Pyramids. General Cone. Right Circular Cone = "Cone"
Aim #6: What are general pyramids and cones? CC Geometry H Do Now: Put the images shown below into the groups (A,B,C and D) based on their properties. Group A: General Cylinders Group B: Prisms Group C:
Unit 3. Chapter 1. Foundations of Geometry. Name. Hour
Unit 3 Chapter 1 Foundations of Geometry Name Hour 1 Geometry Unit 3 Foundations of Geometry Chapter 1 Monday October 1 Tuesday October 2 1.1 Understanding Points, Lines, & Planes 1.2 Linear Measure DHQ
What is a ratio? What is a proportion? Give an example of two ratios that reduce to the same value
Geometry A Chapter 8 8.1 Ratio and Proportion What is a ratio? What is a proportion? Give an example of two ratios that reduce to the same value How do you solve a proportion? ex: 3x + 2 = 5x - 1 4 6 In
Lesson 23: Base Angles of Isosceles Triangles Day 1
Lesson 23: Base Angles of Isosceles Triangles Day 1 Learning Targets I can examine two different proof techniques via a familiar theorem. I can complete proofs involving properties of an isosceles triangle.
Note: Definitions are always reversible (converse is true) but postulates and theorems are not necessarily reversible.
Honors Math 2 Deductive ing and Two-Column Proofs Name: Date: Deductive reasoning is a system of thought in which conclusions are justified by means of previously assumed or proven statements. Every deductive
Geometry 2 nd Semester Review Packet PART 1: Chapter 4
Geometry 2 nd Semester Review Packet PART 1: Chapter 4 Name 1. Determine if these are scale figures. If so state the scale factor, treating the larger image as the original figure, and the smaller as the
4-1 Classifying Triangles. ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240.
ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or. 1. Refer to the figure on page 240. Classify each triangle as acute, equiangular, obtuse, or. Explain your reasoning. 4. equiangular;
Maintaining Mathematical Proficiency
Name ate hapter 8 Maintaining Mathematical Proficiency Tell whether the ratios form a proportion. 1. 16, 4 12 2. 5 45, 6 81. 12 16, 96 100 4. 15 75, 24 100 5. 17 2, 68 128 6. 65 156, 105 252 Find the scale
1.1 Points, Lines, and Planes
1.1 Points, Lines, and Planes Identify and model points, lines and planes. Identify collinear, and coplanar points and intersecting lines and planes in the space. Vocabulary Point, line, plane, collinear,
Date Target Assignment Done! W Review Worksheet. F 9-30 Project Cartoon Enlargement Project. T a 3.
Unit 3 Similar Figures and Dilations 2016-2017 Unit 3 Similar Figures and Dilations Target 1: Use proportions to identify lengths of corresponding parts in similar figures. Target 2: Perform and identify
2.8 Proving angle relationships cont. ink.notebook. September 20, page 82 page cont. page 83. page 84. Standards. Cont.
2.8 Proving angle relationships cont. ink.notebook page 82 page 81 2.8 cont. page 83 page 84 Lesson Objectives Standards Lesson Notes 2.8 Proving Angle Relationships Cont. Press the tabs to view details.
Tools of Geometry 1. X + 9 = 24 2. 25 X = 15 3. X + 3 = -2X -10 4. 3X + 4Y = 2 Place in slope intercept form. 5. Y = ½ X 2 What is the slope? What is the Y- Intercept? Inductive Reasoning is reasoning
Indirect proof. Write indirect proof for the following
Indirect proof Write indirect proof for the following 1.. Practice C A parallelogram is a quadrilateral with two sets of congruent parallel sides. The opposite angles in a parallelogram are congruent.
Unit 1 Geometric Fundamentals
Honors Geometry Unit 1 Geometric Fundamentals Date Target Assignment Done! R 8-17 1.1a 1.1a Worksheet F 8-18 1.1b Pre-Assessment / 1.1b Worksheet M 8-21 1.1 1.2a Worksheet T 8-22 1.2a 1.2b Worksheet W
Geometry Definitions, Postulates, and Theorems. Chapter 3: Parallel and Perpendicular Lines. Section 3.1: Identify Pairs of Lines and Angles.
Geometry Definitions, Postulates, and Theorems Chapter : Parallel and Perpendicular Lines Section.1: Identify Pairs of Lines and Angles Standards: Prepare for 7.0 Students prove and use theorems involving
Unit 1: Foundations of Geometry Section 1: Points, Lines & Planes. The most basic figures in geometry are.
Unit 1: Foundations of Geometry Section 1: Points, Lines & Planes The most basic figures in geometry are. 1 Intersections: Lines Planes Ex #1 2 1a. Name four coplanar points. 1b. Name three lines. 2.Use
Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections. o Combinations of Transformations
Geometry Name Unit 2 Study Guide Topics: Transformations (Activity 9) o Translations o Rotations o Reflections You are allowed a 3 o Combinations of Transformations inch by 5 inch Congruent Polygons (Activities
Angle Bisectors in a Triangle- Teacher
Angle Bisectors in a Triangle- Teacher Concepts Relationship between an angle bisector and the arms of the angle Applying the Angle Bisector Theorem and its converse Materials TI-Nspire Math and Science
Geometry, 8.1: Ratio and Proportion
Geometry, 8.1: Ratio and Proportion Ratio examples: Model car: Recipe: Mix: 1 gallon water The juice from 2 lemons 2 cups sugar This makes 1 gallon of lemonade. What would you mix if you needed to make
Answer Key. 7.1 Forms of Ratios. Chapter 7 Similarity. CK- 12 Basic Geometry Concepts 1. Answers. 1. a) 4: 3. b) 5: 8. c) 6: 19. d) 6: 8: 5 2.
7.1 Forms of Ratios 1. a) 4: 3 b) 5: 8 c) 6: 19 d) 6: 8: 5 2. 1: 1 3. 1: 2 4. 2: 1 5. 1: 1 6. 5: 4: 3 7. 8. 9. 5 12 1 1 19 30 10. 54 and 72 11. 12 and 20 12. 64 and 112 13. 20 14. 240 15. 30 CK- 12 Basic
Geometry Midterm 1-5 STUDY GUIDE
Geometry Midterm 1-5 STUDY GUIDE Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Is the line through points P( 7, 6) and Q(0, 9) parallel to the line through
Math-2 Lesson 8-6 Unit 5 review -midpoint, -distance, -angles, -Parallel lines, -triangle congruence -triangle similarity -properties of
Math- Lesson 8-6 Unit 5 review -midpoint, -distance, -angles, -Parallel lines, -triangle congruence -triangle similarity -properties of parallelograms -properties of Isosceles triangles The distance between
4.6. You would think that determining the tallest building in the world would be pretty. Indirect Measurement. Application of Similar Triangles
Indirect Measurement Application of Similar Triangles.6 Learning Goals Key Term In this lesson, you will: Identify similar triangles to calculate indirect measurements. Use proportions to solve for unknown