Geometry Chapter 1 Basics of Geometry
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1 Geometry Chapter 1 asics of Geometry ssign Section Pages Problems Patterns and Inductive Reasoning o, 25, 34-37, 39, 47, 48 2 ctivity!!! Points, Lines, and Planes odd, 55-59odd Segments and Their Measures 1.4 ngles and Their Measures , 20, 23-33odd, all (skip17), 26-34all 5 QUIZ Logic Puzzle Pg Segment and ngle isectors odd (skip35), 42, 45-53o, 61, ngle Pair Relationships odd, 28, 29-39o, 43-53o, 57, 58, 65-71odd Perimeter, Circumference, rea Review QUIZ all, 31, 33, 34-36all, 41-47o Review Packet 10 Review all 11 CHPTER 1 TEST *For additional chapter 1 review Pg 60-63!* lso check out the website (classzone.com) in the front of your book for more practice In order to receive full credit, assignments must be neat, complete, on time, and all work must be shown. Homework is your practice time, make it worthwhile. ssignments are subject to change. Don t forget to check out classzone.com throughout the chapter for extra practice!
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3 1.1 Patterns of Inductive Reasoning Target goals: Find and describe patterns. Use inductive reasoning to make real-life conjectures. Find a counterexample. Geometry developed when people began recognizing and describing patterns. In this section, you will be describing visual and number patterns. You can use patterns to help make predictions. VOCULRY Conjecture: Inductive Reasoning: Counter Example: DESCRIING VISUL PTTERN: Ex 1: Sketch the next figure in the pattern. Ex 2: Sketch the next figure in the pattern. DESCRIING NUMER PTTERN: Sometimes, patterns allow you to make accurate predictions. Ex 3: Describe a number pattern and then predict the next number. a. 17, 15, 12, 8, b. 48, 16, 16 3, 16, c. 2, 4, 16, 256,.. d. 4, -20, 100, -500,. 9
4 INDUCTIVE RESONING 1) Look for a pattern 2) Make a conjecture 3) Verify the conjecture (re there counter examples?) FINDING COUNTEREXMPLE *To prove that a conjecture is true, you need to prove it is true in LL cases. *To prove that a conjecture is false, you need to provide a single. Ex 4: Find a counterexample to show the conjecture false. Conjecture: The difference of two positive numbers is always positive. Counterexample: The conjecture is.
5 1.2 Points, Lines, and Planes Target goals: Understand and use the basic undefined terms and defined terms of geometry. Sketch the intersections of lines and planes. definition uses known words to describe a new word. In geometry, some words, such as point, line, and plane are undefined terms. lthough these words are not formally defined, it is important to have a general agreement about what each word means. UNDEFINED TERMS: Point: Line: Plane: DEFINED TERMS: Collinear Points: Coplanar Points: Line Segment: Ray: Opposite rays: Ex 1: a. Name three points that are collinear. b. Name four points that are not coplanar. c. Name three points that are not collinear. L R K M P N Ex 2: Complete the following on the Nspire. a. Draw. b. Draw point C so that it is collinear with points and. c. Draw point D not collinear with points,, and C. d. Draw ray D. e. Draw segment CD. f. Name opposite rays.
6 Ex 3: Draw a line. Label three points on the line and name a pair of opposite rays. SKETCHING INTERSECTIONS OF LINES ND PLNES: Two or more geometric figures if they have one or more points in common. The of the figures is the set of points the figures have in common. Ex 4: Draw two intersecting lines. Ex 5: Sketch a line that intersects a plane in one point. Ex 6: Sketch two planes that intersect. Describe their intersection. Ex 7: Sketch two planes that do not intersect. Ex 8: nswer True or False for the following: E F a) Points,, and C are collinear. b) Points,, and C are coplanar. c) Point F lies on DE. d) DE lies on plane DEF. e) D and DE intersect. f) D is the intersection of plane C and plane DEF. D C
7 1.3 Segments and Their Measures Target goals: Use segment postulate. Use the Distance Formula to measure distances. Postulates: vs. Theorems: SEGMENT DDITION POSTULTE: If is between and C, then. If, then is between and C. C Ex 1: RS = TU, ST = 9, RU = 33 R S T a) Find RS b) Find SU. Ex 2: Y is between X and Z. Find the distance between points X and Z if the distance between X and Y is 12 units and the distance between Y and Z is 25 units.
8 USING THE DISTNCE FORMUL Distance Formula If (x 1, y 1 ) and (x 2, y 2 ) are points in a coordinate plane, then the distance between & is. = Ex 3: Find the length of the segments. C = D = (-1, 1) C (3, 2) D (3, -5) Definition: Congruent Segments If two segments are congruent, then. If two segments have, then. If = CD, then. Ex 4: a) In example 3, is C D? b) If D is congruent to C in example 3, then DE =.
9 1.4 ngles and Their Measures Target Goals: Use angle postulates. Classify as acute, right, obtuse, or straight. ngle: C Ex 1: Name 3 different angles. K J L M Measure of an ngle: To indicate the measure of we write. ngles are measured in. Congruent ngles: ngles that have the same measure are. C DEF D 30 C E 30 F Interior and Exterior of an ngle: P Q R djacent ngles: Share a common and, but have no in common. Ex 2: Name the adjacent angles in the figure. X Y W Z
10 NGLE DDITION POSTULTE: R If P is in the interior of RST, then. S T P Ex 3: Find the measure of the following angles: a) m QRS b) If m WXZ 48 and m YXZ 31 then m WXY. R Q T 19 o 23 o S X W Y Z Ex 4: If the m C 88 then, solve for x. (2x) (x - 2) D C CLSSIFYING NGLES: n angle that measures greater than0 and less than 90 is called an angle. n angle that measures 90 is called a angle. n angle that measures greater than 90 and less than 180 is called an angle. n angle that measures 180 is called a angle.
11 1.5 Segment and ngle isectors Target Goals: isect a segment. Use the midpoint formula. isect an angle. Midpoint: If a point is a midpoint of a segment, then it. M If a point, then it is the midpoint. isect: M Segment isector: THE MIDPOINT FORMUL Midpoint Formula If ( x 1, y 1 ) and ( x 2, y 2 ) then M = Ex 1: Find the coordinates of the midpoint of with endpoints (-2, 3) and (5, -2). Ex 2: The midpoint of JK is M(1, 4). One endpoint is J(-3, 2). Find the coordinates of the other endpoint.
12 ISECTING N NGLE: D C ngle isector: If a ray is an angle bisector, then it. If a ray,then it is the angle bisector. Ex 3: RT bisects QRS. Ex 4: KM bisects JKL. Given that m QRS= 60, what are The measures of the two congruent the measures of QRT & TRS? angles are b2x 7g and b4x 41g. Find the measures of JKM and MKL. Ex 5: Name the parts. Ex 6: Find the measure of RST. R 50 o S D C T
13 1.6 ngle Pair Relations Target Goals: Identify vertical angles and linear pairs. Identify complementary and supplementary angles. VERTICL NGLES ND LINER PIRS Linear Pair: **The sum of the measures on angles that form a linear pair is Vertical ngles: Theorem: If two angles are vertical angles, then. Ex 1: In the diagram shown, 1 has a measure of 60. Ex 2: Solve for x. Find the m 2 and m b g 2x 11 Vertical Pairs: Linear Pairs: m 1 = 60 o m 2 = m 3 = m 4 = Ex 3: Solve for x. 3x (2x + 5)
14 COMPLEMENTRY ND SUPPLEMENTRY NGLES: Complementary ngles: If two angles are, then their sum is. If the sum of two angles is, then. 3 4 Complementary angles may either be adjacent or nonadjacent. 1 2 Complementary djacent Complementary Nonadjacent Each angle is the of the other. Supplementary ngles: If two angles are, then their sum is. If the sum of two angles is, then. 7 8 Supplementary angles may either be adjacent or nonadjacent. 5 6 Supplementary djacent Supplementary Nonadjacent Each angle is the of the other. Ex 4: Given that m = 55, find it s complement and it s supplement. Ex 5: X and Y are supplementary. Find the measure of each angle if m X = 6x 1 and m Y = 5x 17. Ex 6: P and Q are complementary. The measure of Q is 4 times the measure of P. Find the measure of each angle.
15 1.7 Perimeter, Circumference, rea Target Goal: Review perimeter, circumference, and area. SQURE P = Side Length: s = RECTNGLE P = Length: Width: w = TRINGLE P = Sides: w, x, & y Height: h = CIRCLE C = Radius: r = DRW SKETCH, WRITE DOWN FORMUL ND FILL IN WHT YOU KNOW. Ex 1: Find the perimeter and the area of a rectangle with a length of 12 inches and a width of 5 inches. Ex 2: Find the radius, circumference, and area for a circle with a diameter of 12 mm. Ex 3: rectangle has an area of 72 ft 2 and a length of 12 ft. Find the perimeter of the rectangle.
16 Ex 4: Find the perimeter and area for the triangle shown. 13 m 12 m 15 m 14 m Ex 5: Find the perimeter and area. 6 cm Ex 6: Find the perimeter and area. 7 in 7 2 in Ex 7: Find the perimeter and area. 5 m 3 m Ex 8: bag of fertilizer covers 1000 square feet. How many bags of fertilizer do you need to cover a yard that is 80 feet by 110 feet. Ex 9: Draw the figure on a coordinate plane, then find it s area. triangle defined by: ( -5, 2) ( 4, 2) C( -1, 6)
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