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17.1 Congruence and Similarity p. 374 Introduction: Quick Review Objective: to learn how to construct congruent line segments and angles Vocabulary: • congruent = line segments and angles having the same length or measure in degrees Guided Learning: Harcourt Math Glossary How to construct a congruent LINE SEGMENT How to construct a congruent ANGLE 17.2 Bisecting Line Segments and Angles p. 380 Introduction: Quick Review Objective: to learn how to bisect line segments and angles by using a compass and ruler Vocabulary: • bisect = divide into TWO congruent parts • midpoint = point halfway between the endpoints of a line segment • perpendicular bisector = line intersecting a line segment at its midpoint to form a 90 degree angle Harcourt Math Glossary How to bisect an angle Congruent and similar shapes Congruent shapes Similar shapes 3 Congruent shapes 4 Start page 1. Which of these shapes are congruent to the yellow one? 1 3 4 2 5 6 7 Hints 5 Answers Start page Congruent shapes are all shown in yellow – were you right? 1 3 4 2 5 6 7 6 Start page What makes a pair of shapes “congruent”? Same angles Same side lengths Can be rotated or a mirror image A cut-out of one shape will always fit exactly over the other • Click the green box if you want to go back to the first “congruent shapes” question page. Question page 7 Start page 2. Which of these shapes are congruent to the yellow one? 4 1 3 2 8 6 5 9 7 8 Answers Start page Congruent shapes are all shown in yellow – were you right? 4 1 3 2 8 6 5 9 7 9 Similar shapes 10 Start page Which of these shapes are similar to the yellow one? 1 3 4 2 5 6 7 Hints 11 Answers Start page Similar shapes are all shown in yellow – were you right? 1 3 4 2 5 6 7 12 Start page What makes a pair of shapes “similar”? Same angles Sides in the same proportion Can be rotated or reflected One is an enlargement of the other Scale factor gives degree of enlargement: – Scale factor 2 → size is doubled – Scale factor 0.5 → size is halved – Scale factor 1 → size doesn’t change → congruent too • Click the green box if you want to go back to the “similar shapes” question page. Question page 13 Start page Using similarity Since shapes are similar, their sides are in the same proportion => 6 = a 9 12 9cm Multiply both sides by 12 => 12 x 6 = a 9 6cm => a = 12 x 2 = 4 x 2 3 1 => a = 8cm 12cm a 14 Start page Which of these shapes are similar to the yellow one? (They aren’t drawn to scale) 12 1 8 9 9 18 2 4 3 6 6 4 12 9 4 6 5 6 4.5 3 15 Answers Start page Similar shapes are shown in yellow – were you right? 12 1 8 9 9 18 2 4 3 6 6 4 12 9 4 6 5 6 4.5 3 16 Start page Scale factor = new value old value. Scale factor? New value = 12 = 3 or 1.5 Old value 8 2 12cm 8cm Scale factor? 5cm New value = 8 = 2 Old value 12 3 7.5cm Can you see the relationship between the two scale factors? 17 Start page Using scale factor Enlarge with scale factor 3 a = 9 x 3 = 27cm 9cm a What will the scale factor be? b SF = new/old = 9/27 = ⅓ OR reciprocal of 3 = ⅓ 15cm b = 15 x ⅓ = 15 ÷ 3 = 5cm 18 Similar shapes - summary c a z b y Ratio a:b:c = ratio x:y:z So: a = x a=x b=y x b y c z c z To see whether 2 shapes are similar, put each ratio in its simplest form and see if they match. Scale factor = new measurement old measurement Old measurement x SF = new measurement new SF old - Scale factor more than 1 => shape gets bigger - Scale factor less than 1 => shape gets smaller - Congruent shapes are similar shapes with SF = 1 Remember: only side lengths change; angles stay the same! 19 16.2 Triangles p. 356 Introduction: Quick Review Objective: learn how to classify triangles and solve problems involving angle measures of triangles Vocabulary: • acute triangle = contains only acute angles • obtuse triangle = contains only one obtuse angle • right triangle = contains only one right angle • equilateral triangle = three congruent sides • isosceles triangle = exactly two congruent sides • scalene triangle = no congruent sides Guided Learning: http://www.mathwarehouse.com/geometry/triangles/interact ive-triangle.htm http://www.hbschool.com/glossary/math2/index6.html http://jmathpage.com/JIMSGeometrypage.html http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/sh apes/play.shtml 16.3 Find a Pattern p. 360 Introduction: Quick Review Objective: learn how to use the strategy “find a pattern” to solve problems Vocabulary: • regular polygon = polygon which all sides and angles are congruent http://www.hbschool.com/glossary/math2/index6.html 16.4 Quadrilaterals p. 362 Introduction: Quick Review Objective: learn how to identify, classify, and compare quadrilaterals http://www.hbschool.com/glossary/math2/index6.html http://jmathpage.com/JIMSGeometrypage.html 16.5 Draw Plane Figures p. 366 Introduction: 1. Quick Review • Objective: learn how to draw plane geometric figures Square Dot Geoboard Square Dot Paper Isometric Dot Geoboard Isometric Dot Paper 16.6 Circles p. 368 Introduction: 1. Quick Review: Complete on your white board 2. Objective: Learn how to identify and draw parts of circles 3. Warm-Up: *Draw a dot on your white board, label it “O”. Next, draw a circle around the center dot you just drew. *Draw a radius and label it “radius” - someone explain how you did it! *Draw a diameter and label it “diameter” - someone explain how you did it! *Draw a chord and label it “chord” - someone explain how you did it! 16.6 Circles continued... Vocabulary: • radius - line segment with one endpoint at the center of a circle and the other endpoint on the circle • diameter - line segment passing through the center of a circle and has both endpoints on the circle • chord - line segment with its endpoints on a circle Harcourt Math Glossary Properties of Polygons Name polygon isosceles triangle scalene triangle equilateral triangle right triangle parallellogram rectangle rhombus square trapezoid Sometimes Always Never