10. Identify an example of each of the

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1 or help with questions 7 to 9, see amples and. 7. Name a pair of similar triangles in each diagram and eplain why they are similar. onnect and pply arefully copy or trace the diagram of the truss bridge. se it to answer questions 0 to. 8. Name a pair of similar triangles in each diagram and eplain why they are similar.. 6 mm 6.7 m W. cm mm J K.0 m M.0 cm V 8 mm.4 m.0 m 9. or each pair of similar triangles in questions 7 and 8, list all the pairs of corresponding angles and corresponding sides.. 7. cm L 9.0 cm G 0. Identify an eample of each of the following. se different colours and/or additional sketches to illustrate your answers. a pair of congruent triangles a pair of congruent rectangles a pair of congruent parallelograms d) a pair of similar triangles e) a set of three similar triangles. Identify a pair of congruent triangles that are related by a translation reflection rotation. escribe the combination of transformations that relates one pair of congruent triangles. escribe a different combination of transformations that relates another pair of congruent triangles.. raw a right triangle. raw a right triangle that is congruent to the one you drew similar to the one you drew neither congruent nor similar to the one you drew 4. re all equilateral triangles similar? Justify your answer.. re all isosceles triangles similar? Justify your answer. 4 MH hapter 7

2 or help with questions to 7, see ample.. how why is similar to. ind the lengths and y. cm 6. he triangles in each pair are similar. ind the unknown side lengths. 7 cm y 7 cm cm f d cm 7. ind the length of in each. cm cm 0 cm or help with question 8, see amples and. 8. ~. ind the area of. 0 cm s r = 7 cm W cm 9 cm ~. ind the area of. d) cm w 9 cm b cm = e) 0 cm 9 cm r p GHI ~ KLM. ind the area of KLM. = cm L M H I G K cm e 0 cm d) ~ Z. ind the area of. cm d 0 cm = 40 cm Z 48 MH hapter 7

3 onnect and pply 9. o measure the height of a tree, ynthia has her little brother,, stand so that the tip of his shadow coincides with the tip of the tree s shadow, at point.. Melanie is designing a crest for her hockey team, the rigazoids. Her prototype consists of four congruent equilateral triangles. h = 8.7 cm ynthia s brother, who is. m tall, is 4. m from ynthia, who is standing at, and 6. m from the base of the tree. ind the height of the tree,. 0. ind the width of the canyon. b = 0 cm What is the total area of this crest? What is the area of the green section? the purple sections? What is the area of a giant similar crest with base 0 cm? d) What is the height of a similar crest with area 00 cm?. he front of each brick in the fireplace measures 0 cm by 0 cm. m m 60 m. se the dimensions of the surveyors triangles to find the width of the river, to the nearest metre. 0 m m 7 m width =? How many similar rectangles of different sizes can you find? ketch a diagram to illustrate them. Label their dimensions (length and width). What is the area of the front of one brick? ind the area of the entire fireplace, including the opening. d) ind the area of the opening. e) ind the area of the fireplace, ecluding the opening. 4. ind the length and width of the pond. he following measures are known: 4 m m ssume that is a line of symmetry for the pond. 7. se imilar riangles to olve roblems MH 49

4 6 ; 9..6 ;.4 or ; 9 8 ; 97 d) e) m,.4 m. $.0 ; 6 8 ; Investigate roperties of imilar riangles, pages 0. nswers will vary.. nswers will vary.. nswers may vary. hapter 7 Get eady, pages 6 9. c, n 0, 0 a 0, y 0, m 68 e 4, r 8 d) f 0, u 70, h, p e) k 7, v 6. nswers may vary. or eample: he three interior angles of an equilateral triangle are all equal. Let one interior angle be. ince the sum of the interior angles in a triangle is 80, 80. hen, 80. his equation can be solved to give 60. he three equal interior angles in an equilateral triangle are all 60.. nswers may vary. or eample: ince the sum of the interior angles in a triangle is 80, y his equation can be solved to give y 90. he two acute angles in a right triangle are complementary. 4. nswers may vary. or eample: Let the third interior angle be c. ince the sum of the interior angles in a triangle is 80, a b c 80. his equation can be solved to give c 80 (a. ince the angles c and are supplementary, c 80. ubstitute the value for c into this equation to get 80 (a a b a b he eterior angle of a triangle is equal to the sum of the two opposite interior angles m m No. es. 9. y 4. a d) 4 or 0. nswers will vary.. : nswers may vary. or eample: 900 km; 00 km nswers will vary.. reflection translation dilatation d) rotation. nswers will vary. 4. nswers will vary. 4. nswers may vary. or eample: ongruent figures, because the tiles will be the same, or similar figures if the sides are in proportion. imilar figures, because the logo on the shoulder would be smaller than the logo on the chest, but the same shape. Neither, because the door would be rectangular and the window might be a square. he figures could also be similar figures, or congruent figures. d) imilar figures, because the three-dimensional model will be smaller than the real building, but the same shape.. ~ KLM J ~ GN V ~ VW d) ~ J J 6. KL LM KM G G N V V d) V VW W 7. ~ ; and because they are alternate angles. lso, because they are opposite angles. ~ ; is common to both triangles; and because they are corresponding angles of parallel lines. V ~ WV; V is common to both triangles, because they are both right angles. lso, W because they are corresponding angles of parallel lines. 8. ~ ; ratios of corresponding sides are all ~ G; ratios of corresponding sides are all JKM ~ LJM; ratios of corresponding sides are all nswers MH

5 9. or question 7 :,, ; : : :,, ; : : : W,, V WV; :W V:V V:WV or question 8 :,, ; : : : G, G, G; :G :G : KJM JLM, JKM LJM, JMK LMJ; JK:LJ KM:JM JM:LM 0. nswers will vary.. nswers will vary.. nswers may vary. or eample: reflection or translation nswers may vary. or eample: rotation or dilatation. nswers will vary. 4. nswers may vary. or eample: es, because the corresponding interior angles will be equal (60 ) and the ratios of corresponding side lengths will be equal.. nswers may vary. or eample: No, because the two equal angles in an isosceles triangle may not equal the two equal angles in a different isosceles triangle. 6. nswers may vary. or eample: translation 7. l 9.0 cm, h., w. l 7.0 cm, h 0., w kg se imilar riangles to olve roblems, pages 4. 6, cm cm. area of first triangle, area of similar triangle he area of the larger triangle is 6 times as great as the area of the smaller triangle. nswers may vary. or eample: 6 is the square of the scale factor, 6.. nswers will vary. 4. nswers will vary.. ~ because and because they are corresponding angles of parallel lines, and because they are opposite angles. 0 cm, y 6. d, f s, r 0 cm b 7. cm, w d) p 6.7 cm, r 7. cm e) d. cm, e cm 7. 9 cm 8. 7 cm d). 9.. m m. 44 m. 4. cm 7 0 cm ; 8 8 cm 9. cm d) 9. cm 6 MH nswers. nswers may vary. or eample: 6; 0 0, 0 0, 0 40, 0 60, 0 80, 0 00, 0 0, 0 40, 0 60, 40 40, 40 60, 40 80, 40 00, 40 0, 40 40, cm 800 cm d) 00 cm e) 9600 cm 4. length m, width 8.7 m. nswers will vary cm 7. nswers may vary. or eample: Let the first right triangle have base b, height h, and area. bh hen the similar right triangle has base kb and height kh, since k is the scale factor that relates the corresponding side lengths. he area of the similar triangle is (base)(height) (k(kh) (k )(bh) k a bhb k. he areas of two similar right triangles are related by the square of the scale factor, k. 8. nswers will vary. nswers will vary. nswers may vary. or eample: he ratio of the rea areas of the triangles is k. k rea 9. : 0. nswers may vary. or eample: Let the second triangle have side lengths a, b, and c. hen, the second triangle has corresponding side lengths of a, b, and c. hen, the two perimeters are a b c and a b c (a b he ratio of the perimeters is :, or :.. nswers will vary.. Happy Valley/Goose ay m. 0 km 6. nswers may vary. or eample: arth is round and not flat. nswers will vary : m h