1. 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: Review divisibility rules (slide 2) Review EXAMPLES A. and B. -- How did you decide 610 was not divisible by 3? Harcourt Math Glossary Similarity vs. Congruence Demo How to construct a congruent LINE SEGMENT How to construct a congruent ANGLE

2. 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 Review divisibility rules (slide 2) Review EXAMPLES A. and B. -- How did you decide 610 was not divisible by 3? Harcourt Math Glossary How to bisect a line segment How to bisect an angle

3. 3 Congruent and similar shapes Congruent shapes Similar shapes

4. 4 Congruent shapes

5. 5 1. Which of these shapes are congruent to the yellow one? 2 5 4 3 1 7 6 8 Answers Hints Start page

6. 6 Congruent shapes are all shown in yellow – were you right? 5 4 3 1 7 6 8 Start page 2

7. 7 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. Click the green box if you want to go back to the first “congruent shapes” question page. Question page Start page

8. 8 2. Which of these shapes are congruent to the yellow one? Answers Start page 2 5 1 3 4 6 7 8 9

9. 9 Congruent shapes are all shown in yellow – were you right? Start page 2 5 1 3 4 6 7 8 9

10. 10 Similar shapes

11. 11 Which of these shapes are similar to the yellow one? 2 5 4 3 1 7 6 8 Answers Hints Start page

12. 12 Similar shapes are all shown in yellow – were you right? 2 5 4 3 1 7 6 8 Start page

13. 13 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. Click the green box if you want to go back to the “similar shapes” question page. Question page Start page

14. 14 Using similarity 9cm 12cm 6cm a Since shapes are similar, their sides are in the same proportion Multiply both sides by 12 => 12 x 6 = a 9 => a = 12 x 2 = 4 x 2 3 1 Start page => 6 = a 9 12 => a = 8cm

15. 15 Which of these shapes are similar to the yellow one? (They aren’t drawn to scale) 4 3 2 1 5 6 Answers Start page 6 9 6 9 4 6 4.5 3 12 18 9 12 4 8

16. 16 Similar shapes are shown in yellow – were you right? Start page 9 6 5 6 9 6 4.5 3 3 12 18 1 9 12 4 6 4 2 4 8

17. 17 Scale factor = new value old value. 8cm 12cm Scale factor? 5cm 7.5cm New value = Old value New value = Old value Start page 12 = 3 or 1.5 8 2 Can you see the relationship between the two scale factors? 8 = 2 12 3

18. 18 Using scale factor 9cm a Enlarge with scale factor 3 b 15cm a = 9 x 3 = 27cm SF = new/old = 9/27 = ⅓ What will the scale factor be? b = 15 x ⅓ = 15 ÷ 3 = 5cm Start page OR reciprocal of 3 = ⅓

19. 19 Similar shapes - summary a b c x y z Ratio a:b:c = ratio x:y:z So: a = xa = x b = y b yc 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 - Scale factor more than 1 => shape gets bigger - Scale factor less than 1 => shape gets smaller - Congruent shapes are similar shapes with SF = 1 Old measurement x SF = new measurement Remember: only side lengths change; angles stay the same! SF new old

20. 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: Review divisibility rules (slide 2) Review EXAMPLES A. and B. -- How did you decide 610 was not divisible by 3? http://www.hbschool.com/glossary/math2/index6.html http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/sh apes/play.shtml http://www.mathwarehouse.com/geometry/triangles/interact ive-triangle.htm http://jmathpage.com/JIMSGeometrypage.html

21. 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

22. 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

23. 16.5 Draw Plane Figures p. 366 Introduction: 1. Quick Review Objective: learn how to draw plane geometric figures Square Dot Geoboard Isometric Dot Paper Square Dot Paper Isometric Dot Geoboard

24. 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!

25. 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

26. Properties of Polygons Name SometimesAlwaysNever polygon isosceles triangle scalene triangle equilateral triangle right triangle parallellogram rectangle rhombus square trapezoid