Name:________________________________________
Date:________ Period:_______
Similar Triangles Review Sheet
Ms. Anderle
Similar Triangles: Review
The exam will consist of 15 multiple choice questions (including review questions) worth a total of 45
points and 7 Part II questions. There will be 2 formal similar triangle proofs and 1 informal similar
triangle proof. Along with this review sheet, review all class notes.
1. The ratio of the surface areas of two similar spheres is
. If the volume of the smaller sphere is 40 m3,
what is the volume of the larger sphere? (round to the nearest tenth, if necessary).
2. The ratio of the perimeters of two similar rectangles is
. If the area of the larger rectangle is 121
cm2, what is the area of the smaller rectangle? (round to the nearest tenth, if necessary).
3. The ratio of the areas of two similar prisms is
. What is the ratio of the volumes?
4. The accompanying diagram shows a 24-foot ladder leaning against a building. A steel brace extends
from the ladder to a point where the building meets the ground. The brace forms a right angle with the
ladder. If the steel brace is connected to the ladder at a point that is 10-feet from the foot of the ladder,
find the value of x.
5. The sides of a quadrilateral measure 12, 18, 20, and 16. If the shortest side of a similar quadrilateral
measures 3, find the measures of the remaining sides of this quadrilateral. What is the ratio of similitude
between the two quadrilaterals?
6. In the diagram below, DE = x, AC = x + 10, BD = 4, and DB = 6. Find the value of x.
7. In the diagram below, the length of DB = 2, BE = 5, and EC = 8. What is the length of DA? (round to the
nearest tenth, if necessary).
8. Determine whether or not ΔABC~ΔDEF. Show proof of why or why not.
A
16
C
F
9
E
12
8
12
6
D
B
9. Given: PR = 14, PQ = 12, QR = 6, XZ = 7, XY = 6, YZ = 3.
Prove: ΔPQR~ΔXYZ
10. Given:
D
Prove: AB•EC=ED•AC
A
C
E
B
11. Given: <B <D
A
E
B
F
Prove:
D
C
12. Is ∆I ~ ∆II? Explain
20
6
I
II
8
13.
A
D
B
15
Given: DE || BC
E
Prove: AD x AC = AB x AE
C