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Chapter 6: Similar Triangles
Review Sheet
TEST: MONDAY 01/11/2015
ALWAYS draw diagrams if one does not exist. ALWAYS label everything that you can. Remember,
diagrams are not to scale! Don’t trust what you see; only rely on the information that provided in the
question.
All work must be done on a separate sheet of paper (you may mark diagrams on here). Turn in on test
day for a +5 bonus. Check your answers online!!
Ratios of Similitude
1. The sides of a triangle are 5, 6, and 10. Find the longest side of a similar triangle when the shortest side
is 15.
2. Two triangles are similar. The lengths of the sides of the smaller triangle are 4, 6, 7. The shortest side of
the larger triangle is 16. What are the remaining sides of the larger triangle?
3. A boy looks into a mirror that has been placed on the ground 3 meters away and sees the reflections of
the top of a telephone pole. If the mirror is 21 meters away from the telephone pole and the person is 2
meters tall, how tall is the telephone pole?
4. The sides of a quadrilateral measure 12, 15, 24 and 18. If the shortest side of a similar quadrilateral
measures 4, find the measures of the remaining sides of the quadrilateral. What is the larger figure’s
perimeter?
5. If ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹 and 𝐴𝐵 = 26, 𝐴𝐶 = 18, and 𝐷𝐹 = 12, what is the length of DE to the nearest tenth?
a. 8.3
b. 16.5
c. 17.3
d. 39
6. Henry casts a shadow that is 3 feet in length. His son, who is 3.5 feet tall, casts a shadow that is 1.8 feet
in length. How tall is Henry? (to the nearest tenth of a foot).
7. ∆𝑃𝑄𝑅~∆𝑆𝑇𝑈. Find the perimeter of ∆𝑆𝑇𝑈
Overlapping Triangles
ALWAYS ALWAYS ALWAYS redraw as two separate triangles. NO EXCEPTIONS!
8. Find the length of AE
9. Find the length of FJ
10. Find the value of x
11. Find the value of x to the nearest tenth.
12. Find the value of the height in the following diagram at which the tennis ball must be hit so that it will
just pass over the net and land 6 meters away from the base of the net.
Midsegments
13. In the diagram below, the vertices of ∆𝐷𝐸𝐹 are the midpoints of the sides of equilateral triangle ABC,
and the perimeter of ∆𝐴𝐵𝐶 is 36cm.
What is the length of EF?
a. 6
b. 12
c. 18
d. 4
14. In the diagram below of ∆𝐴𝐶𝑇, D is the midpoint of AC, O is the midpoint of AT, and G is the midpoint
of CT. If AC=10, AT=18, and CT=22, what is the perimeter of parallelogram CDOG?
15. MT is a midsegment of ∆𝐿𝑈𝑉. Use the diagram to answer the following questions.
a. What is the measure of ∠𝑈?
b. What is the measure of ∠𝑉?
c. What is the measure of 𝑇𝑀𝑈?
16. A student makes the rabbit shadow that you see in the diagram. The part of his hand making the
shadow is 4.5 inches tall and it is halfway between the flashlight and the wall. The top of his fingers
are halfway between the flashlight and the top of the shadow. How tall is the shadow rabbit?
17. X, Y, and X are midpoints of the sides of the triangle ABC. 𝑋𝑌 = 3𝑘 − 1, and 𝐴𝐶 = 5𝑘 + 7.
How long is XY?
Ratio of Similarity
Remember: No matter what information is given, get down to the basic ratio of similitude to start
18. If the ratio of the surface area of two similar cylinders is 16:25, what is the ratio of their volumes?
19. If the ratio of the perimeters of two similar triangles is 2:9, what is the ratio of their areas?
20. If the ratio of the volumes of two similar spheres is 125:8, what is the ratio of their areas?
21. If the ratio of the surface areas of two similar rectangular boxes is 4:9, what is the volume of the
larger box if the volume of the smaller box is 26 m3? (round to the nearest tenth, if necessary)
22. If the ratio of the volumes of two cylinders is 8 : 343, what is the area of the smaller cylinder if the
area of the larger cylinder is 98 m2?
23. If the ratio of the perimeters of two similar spheres is 4 : 5, what is the volume of the larger sphere if
the volume of the smaller sphere is 75 in3 ? If necessary, round your answer to the nearest
hundredth.
Informal Similarity Proofs
24. ∆𝑋𝑌𝑍 has angles with measures of 60 and 80 degrees. ∆𝑈𝑉𝑊 has angles with measures of 80 and 50
degrees. Are the triangles similar? Explain.
25. Show that the two triangles are similar.
26. Determine if the right triangles below are
similar. Explain.
27. Is ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹? Explain
28. Is ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹? Explain