lkueh.files. web viewcynthia’s brother, who is 1.2 m tall, is 4.2 m from cynthia, who is...
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MPM2D Similar and Congruent Triangles Worksheet
Pre-practice (Optional):1. For the triangles below, name the similar triangles in each case. Write the letters so that
equal angles appear in corresponding order.
2. For each pair of similar triangles in question 1, write the equivalent ratios of side
lengths.3. The triangles in each pair are similar. Find the unknown side lengths.
Mandatory Practice (no calculator):
4. Find the length of x in each.
5. Use the dimensions of the surveyors’ triangles to find the width of the river, to the nearest metre.
6. Find the length and width of the pond. The following measures are known: AB=14m BC=11m Assume that XY is a line of symmetry for the pond.
7. To measure the height of a tree, Cynthia has her little brother, BR, stand so that the tip of his shadow coincides with the tip of the tree’s shadow, at point C.
Cynthia’s brother, who is 1.2m tall, is 4.2m from Cynthia, who is standing at C. and 6.5m from the base of the tree. Find the height of the tree, TE.
8. Solve a5−a6=1 then check by substituting.
9. Factor 24 x3−116 x2+140 x
10. Evaluate (4−7 )2−(7−3 )2
11. Determine the number of solutions to the linear system x+ y=6 and x− y=2.
12. Factor 9 x2−60 x+100
Answers:1. a) ΔABC~ΔKLM b) ΔTJP~ΔRGN c) ΔTVX~ΔUVS d) ΔABC~ΔEDC
2. a) ABKL
= BCLM
= ACKM b)
TJRG
= JPGN
= TPRN c)
TVUV
=VXVS
=TXUS d)
ABED
= BCDC
= ACEC
3. a) d=14cm , f=8 cm b) s=6cm, r=30cm c) b=7.5cm ,w=6 cm
4. a) 8cm b) 9cm
5. 44m 6. length 22m, width 17.4m
7. 3.1m
8. a=30
9. 4 x(2 x−5)(3 x−7)
10. −7
11. One solution - make both equations y=mx+b form then compare slopes. Slopes are not equal so the lines intersect once.
12. (3 x−10 )2