Name:_______________________
Similar Triangles Test: Review
Date:_____ Period:____
Ms. Anderle
Similar Triangles Test: Review
The exam is worth 95 points.
It will consist of:
1) 15 multiple choice questions (total of 45 points)
a. Review Questions – mean proportional, converse, inverse,
contrapositive, negation, simplest radical form, 30-60-90 triangle,
45-45-90 triangle, and supplementary/complementary angles.
b. Similar Triangle Questions – ratio of similarity/ratio of
perimeters/ratio of areas/ratio of volumes, and find the missing
side of similar triangles
2) Part II Questions (total of 50 points)
a. Leg Rule/Altitude Rude
b. Not-So-Formal Proof
c. Overlapping Triangles (find the missing measure)
d. Formal Similar Triangle Proofs
i. Parallelogram
ii. Product of the means/product of the extremes
iii. Corresponding sides of similar triangles are in proportion
Review Questions:
1) Triangle ABC is a 30-60-90 right triangle. <A is the 30 degree angle, <B is the 60
degree angle, and <C is the right angle. If side AB = 10. What is the length of side
BC and AC?
2) Triangle MAY is an isosceles right triangle. If the sides opposite the two base
angles measure 4 inches, what is the length of the third side of the triangle?
3) Given the statement: “If today is March 11th, then I am at a concert,” write the
converse, inverse, and contrapositive of the statement.
Converse: ______________________________________________________
Inverse: _______________________________________________________
Contrapositive: __________________________________________________
Which statement is logically equivalent to the original? ____________________
4) What is the sum of √27 and √12?
5) What is √125 in simplest radical form?
6) The measure of two supplementary angles are in the ratio 3:7. What is the
measure of both angles?
7) The measure of two complementary angles are in the ratio 2:3. Find the measure
of the smaller angle.
8) What is the geometric mean between 4 and 8. (round to the nearest tenth)
9) Name the 5 ways to prove triangles congruent.
10) If the ratio of the surface area of two similar cylinders is 16:25, what is the
ratio of their volumes?
11) If the ratio of the perimeters of two similar triangles is 2:9, what is the ratio
of their areas?
12) If the ratio of the volumes of two similar spheres is 125:8, what is the ratio of
their areas?
13) If the ratio of the surface areas of two similar rectangular boxes is 4:9, what
is the volume of the larger box is the volume of the smaller box is 26 m 3? (round to
the nearest tenth, if necessary)
14) 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?
15) The sides of a triangle are 5, 6, and 10. Find the longest side of the triangle, if
the shortest side is 15.
16)
DB = 3, DA = x, DE = x, and AC = 6
a) Find the value of x:
b) Find the scale factor:
17) Find the value of BC using the diagram below:
18) Is ∆I ~ ∆II? Explain
I
6
8
20
II
15
19) Prove ∆I ~ ∆II. Explain why.
12
12
I
21
16
II
28
9
20)
A
D
B
Given: DE || BC
E
Prove: AD x AC = AB x AE
C
21)
A
B
Given: Quad ABCD is a parallelogram
Prove: AB = AD
DC
BC
D
C
In addition to these problems, review the pages we did in your workbook and all of
the notes.
Good Luck on the Exam!!!