# WS- U7- Similiarity

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```					           Math 9    9SS3 – Similarity
Name:                                                                                          /35

9SS3 – Demonstrate an understanding of similarity of polygons

Part I: Review

1. If the perimeter of a rectangle is 64 cm, then the dimensions that would give the greatest
possible area are

a.   1 cm by 31 cm
b.   1 cm by 63 cm
c.   16 cm by 16 cm
d.   32 cm by 32 cm

2. If the angles of a triangle have a ratio of 1:2:6, then the measure of the largest angle is

a.   20o
b.   40o
c.   120o
d.   140o

3. If the perimeter of a rectangle is 32 cm, then the dimensions that would give the greatest
possible area are

A.   1 cm by 15 cm
B.   1 cm by 31 cm
C.   8 cm by 8 cm
D.   16 cm by 16 cm

Part II:
4. The following triangles in each pair are similar. Find the unknown side lengths. Show your
work for full marks. (2 marks each)

a.                                                c.

b.                                                d.
5. Find   in each of the following. Show all of your work for full marks. (1 mark each)

a.

b.

6. The 5 m flagpole casts a 4 m shadow at the same time of day as a building casts a 30 m
shadow. How tall is the building? (1 mark)

7. Surveyors have laid out triangles to find the length of the lake. Calculate this length. Show
all of your work for full marks. (1 mark)
8. Surveyors have laid out these triangles to calculate the width of a canyon. Find this width to
the nearest metre. Show all of your work for full marks. (1 mark)

9. If Δ    and Δ     are similar triangles, then what is the length, to the nearest tenth of a
numerical response section below. (1 mark)

10. Complete the following ratios for each pair of similar triangles below. An example has been
given. (10 marks)

a.

b.
11. The triangles in each of the following pairs are similar. Find all of the unknown side lengths
for each. Round your answer to the nearest tenth and show your work for full marks. (2
marks each)

a.

_______________                        _______________

b.

_______________                        _______________
12. Explain why Δ   is similar to Δ       . (2 marks)

13. Find   in the following. Show all of your work for full marks. (1 mark)

14. Find   and   in the following. (2 marks)
15. Jim wants to measure the width of a small river that is near his house. He draws this
diagram based on measurements that he knows, where A, B, and C represent points in a
nearby park. What is the width of the river. Round your answer to the nearest metre and
show your work for full marks. (1 mark)

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