Download Chapter 5 Review Sheet

Honors Geometry
Chapter 5 Review Sheet
Name: _____________________________________
1. In ΔXYZ, ZX  XY  YZ
a) List the angles in order from least to greatest.
b) XZ = 3x – 6 and ZY = x + 8
c) What are the restrictions on x?
A
2. Given: AD is the median to BC.
AD  3 x  2
BD  5 x  3
DC  2 x  6
Find the length of AD.
B
D
C
3. Write a compound inequality for the possible measures of L.
4. List the angles of ∆GHI in order from smallest to largest measure.
5. List the sides of ∆PQR in order from shortest to longest.
For numbers 6 & 7, fill in the blank to complete each sentence.
6. A(n) __________________ is a segment that joins a vertex of a triangle and is perpendicular to the side opposite to the vertex.
7. The ____________________ of a triangle is equidistant from the vertices of the triangle.
8. Write an inequality relating m∠1 to m∠2.
9. Write an inequality relating AB to DE.
10. Write an inequality about the length of GH .
11. Complete the proof by supplying the missing information for each corresponding location.
Given: AB = DE, and BE > AD
Prove: mCAE > mCEA
Statements
1. AB = DE
Reasons
1. Given
2. BE > AD
2. Given
3. AB  DE
3. Def. of  segments
4. __________________________
4. Reflexive Prop.
5. mCAE > mCEA
5. ____________________________________
12. The vertices of ∆XYZ are X(0, 4), Y(6, 12), and Z(12, 2). Find the coordinates of the centroid of ∆XYZ.
13. Write a valid inequality of the restrictions on x.
(5x – 10)°
14. The perpendicular bisectors of ∆ABC meet at point G. Find GC.
AD = 24, BG = 25, GH = 7.
(2x)°
A
2
D
2
B
C
G
R
7
H
15. The angle bisectors of ∆ABC meet at point G. Find GD.
A
12
AD = 12, BG = 15, GH = 9.
D
C
G
R
1
9
H
B
16. P is the circumcenter of ∆XYZ. Find PZ.
SX = 3, SP = 4, RZ = 12.
X
3
S
R
4
12
P
Y
Z
17. P is the incenter of ∆XYZ and ZP = 15, XN = 24, and XP = 26. Find PO.
X
M
26
24
P
Y
N
15
O
Z
Use the following information for numbers 18 – 22: L is the centroid of ∆MNO, NP = 14, ML = 20, and NL = 9.
18. PO = ? .
M
19. MP =
? .
R
20. NQ =
? .
21. LQ =
? .
22. Perimeter of ∆NLP
20
Q
L
9
N
? .
14
P
O