Download Geometry Review Name A# ______ Which of the following is not

Geometry Review
1. Which of the following is not true about the
medians of a triangle?
a. Regardless of the triangle’s shape, the three
medians always meet at a single point.
b. The point where the medians intersect is
called an incenter.
c. The point where the medians intersect is
called a centroid.
Name ____________________________________ A# ________
2. Which of the following is unnecessary to prove
that the 2 base angles of an isosceles triangle are
congruent?
a. The angle sum theorem for triangles
b. SAS postulate
c. The definition of an angle bisector
d. The definition of congruent triangles
d. A triangle has three medians.
3. Which of the following is necessary to prove that
a triangle’s exterior angle equals the sum of the
two remote interior angles?
a. The definition of complementary angles
b. The definition of an angle bisector
4. Similar triangles are triangles that are the same
shape but not the same size. How can we
determine whether triangles are similar or not?
a. The ratio between each corresponding side
is the same.
c. The definition of supplementary angles
b. One would lie directly on top of the other
and match precisely.
d. The definition of congruent triangles
c. All three angles are equal.
d. Both a. and c. are correct.
5. A segment connects the midpoints of two sides of
a triangle. What is true about this segment?
a. It is always horizontal and half the length of
each side.
b. It is always perpendicular to the two sides it
joins and forms an isosceles triangle with
the portions of the sides above it.
c. It is always parallel to the third side and half
as long as the third side.
d. It is always half the length of those two sides
and parallel to the third.
6. Assuming that ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐷𝐶 and that the two
triangles in the figure are similar, which
triangle is similar to ∆𝐴𝐵𝐸?
D
a. ∆𝐶𝐷𝐸
E
A
C
b. ∆𝐷𝐸𝐶
c. ∆𝐸𝐷𝐶
B
d. All of the above
7. Mike has to build two similar tents for his buddy
Jim. Both tents have a 70° angle at the top. He
asks Jim for the blueprints, and Jim gives him the
diagrams below. What are the side lengths of the
larger tent?
D
A
6 ft
B
70°
7.47 ft
70°
y
6.96ft
C
8. In the diagram below, what is the measure of
∠𝐸 if the two triangles are similar?
D
z
A
F
11.21 ft
B
E
a. 6 ft, 6.96 ft, and 7.47 ft
b. 8 ft, 9.96 ft, and 11.21 ft
c. 9 ft, 10.44 ft, and 11.21 ft
d. 10 ft, 11.21 ft, and 12.63 ft
̅̅̅̅ into
9. A line parallel to a triangle’s side splits 𝐴𝐵
̅̅̅̅
lengths 12 and 5. The other side, 𝐴𝐶 , is split into
lengths of x and 10. What is the length of ̅̅̅̅
𝐴𝐶 ?
30°
C
F
E
a. 30°
b. 60°
c. 70°
d. 90°
10. The hypotenuse of a right triangle has length 13
units, and one leg has length 12 units. How long
is the other leg?
11. Given EFGH is a square with a diagonal drawn
12. What is the measure of a central angle with an
from ∠𝐸 to ∠𝐺. Complete the proof that ∆𝐸𝐹𝐺 ≅
arc measure of 45°?
∆𝐺𝐻𝐸.
̅̅̅̅ and 𝐹𝐺
̅̅̅̅ ≅ 𝐻𝐸
̅̅̅̅ ≅ 𝐺𝐻
̅̅̅̅ true? Why?
a. Is 𝐸𝐹
b. Is ̅̅̅̅
𝐸𝐺 ≅ ̅̅̅̅
𝐸𝐺 true? Why?
c. Is ∆𝐸𝐹𝐺 ≅ ∆𝐺𝐻𝐸 true? Why?
13. What is the measure of an inscribed angle with
arc measurement of 70°?
14. What is the measure of the arc with an inscribed
angle of 18°?
15. What is the measure of the major arc formed by 16. What is the measure of the angle formed
two tangents that are perpendicular to one
between a tangent and the diameter of a circle?
another?
17. Given an arc length of 20 ft and 𝜃 = 90°, find
the radius of the circle.
𝜋
19. Given a radius with length 4.5 in and 𝜃 = 6 , find
the area of the sector.
18. Given an arc length of 43.2 m and a radius of 21.
4 m, find 𝜃.
20. What is the equation of the circle with center at
(4, -3) and radius of 2?
a. (𝑥 − 4)2 + (𝑦 + 3)2 = 2
b. (𝑥 − 4)2 + (𝑦 + 3)2 = 4
c. (𝑥 + 4)2 + (𝑦 − 3)2 = 4
d. (𝑥 − 4)2 − (𝑦 − 3)2 = 4
21. What are the center and radius of the circle
described by the equation
𝑥 2 + 𝑦 2 − 18𝑥 + 12𝑦 + 68 = 0?
22. What is the equation for the circle centered on W
̅̅̅̅̅?
with radius 𝑊𝑍
a. Center (6, -9); radius 7
W
b. Center (-9, 6); radius 7
c. Center (-6, 9); radius 7
d. Center (9, -6); radius 7
Z
a. (𝑥 − 2)2 + (𝑦 − 4)2 = √125
b. (𝑥 − 2)2 + (𝑦 − 4)2 = 125
c. (𝑥 + 3)2 + (𝑦 + 6)2 = √125
d. (𝑥 + 3)2 + (𝑦 + 6)2 = 125
23. A triangle has a perimeter of 100
24. Shmikea, the newly imported Norwegian
centimeters and one side is 35 centimeters.
superstore sells beautiful 6-foot round shag
The other two sides have a ratio of 5:8. What
rugs. Borg’s living room is a 12 by 18 foot
is the length of the longest side of the
rectangle, and his goal is to cover as much of the
triangle?
floor as possible with these rugs without them
overlapping. How much of the floor space will be
a. 65 centimeters
left uncovered if he goes through with his plan?
(Use the approximation 𝜋 = 3.14.)
b. 40 centimeters
a. 7.74 ft2
c. 35 centimeters
b. 46.44 ft2
d. 5 centimeters
c. 169.56 ft2
d. 216 ft2
25.
̅̅̅̅ .
Given ADBC is a parallelogram. Prove ̅̅̅̅
𝐴𝐸 = 𝐸𝐶
E