Download Geometry

Geometry
Name___________________
Chapter 3 Review
Date__________ Period____
For questions 1 – 5, write A for always, S for sometimes, or N for never.
1. A right triangle has three right angles.
______
2. An isosceles triangle is a right triangle.
______
3. The base of an acute isosceles triangle is shorter than either leg. ______
4. The altitude of a triangle bisects the side to which it is drawn.
______
5. A median of a triangle bisects the angle it is drawn from.
______
6. List the three ways to classify a triangle by side length.
7. Write the definition of an altitude and a median.
8. What information is needed to prove these two triangles congruent using HL
postulate.
9. Name the base angles if LB  BE
10. In the diagram, if UM  AS then what property justifies UA  MS .
Solve problems 11 and 12 by referring to the diagram and the information given
W
Given: ASU  WIN
15
4x + 6 S
11. Find the measure of W . ______
10
A
28 91
12. Solve for x:
I
61
U
13. Given: 5  6
HN is the altitude to AD
Prove: Triangle HAD is isosceles.


Statement
Reason
1.
2.
3.
4.
5.
6.
7.
8.
9.
14. Given: NE  SE
EO is an altitude.
Prove: EO bisects NES

1.
2.
3.
4.
5.
6.
7.
8.
9.
Statement
Reason
6
N
In problems 15-18 “mark” the diagram with the given information and then state
the reason for the congruence (SSS, SAS, ASA, or HL).
3
15.
1
2
______
B
16.
______
4
A
1  2 and 3  4
C
D
BD is an altitude of ABC
AD  DC
17.
______
A
E
18. A
______
B
B
C
D
C
ED  BC
A
D
E
C is the midpoint of AE and DB
19. Reflect the following triangle over the y-axis; write the coordinates of the new
triangle.
In problems 20-25 name the triangles that are congruent and give the appropriate
congruence theorem (SSS, SAS, ASA, or HL).
20.
ABC  __________
ABC  __________
21.
_________________
_________________
22.
ABC  __________
ABC  __________
23.
_________________
_________________
24.
ABC  __________
ABC  __________
25.
_________________
_________________
26. The perimeter of NAU is 55. NA = x + 4, AU = 24, and NU = 5x + 3. By solving
for x, determine whether NAU is scalene, isosceles, or equilateral.
A
24
x+4
N
U
5x + 3
27. In triangle with vertices A, B, and C, angles B and C are congruent. AB = 6x +7,
AC = 5x + 11 and BC is 3x + 2y. How long is BC in terms of “y”?