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.
6. Name the shortest and the longest segments.
For numbers 7 & 8, determine whether each sentence is true or false. If it is false, replace the underlined word to make a true sentence.
7. The altitude of a triangle is a segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex.
8. The centroid of a triangle is the point where the altitudes of the triangle intersect.
For numbers 9 – 11, choose the correct term to complete each sentence.
9. The point of concurrency of the perpendicular bisectors of a triangle is called the (circumcenter, median).
10. The (incenter, orthocenter) of a triangle is the intersection of the angle bisectors of the triangle.
11. The sum of the measures of any two sides of a triangle is (greater, less) than the measure of the third side.
For numbers 12 & 13, fill in the blank to complete each sentence.
12. A(n) __________________ is a segment that joins a vertex of a triangle and is perpendicular to the side opposite to the vertex.
13. The ____________________ of a triangle is equidistant from the vertices of the triangle.
14. Write an inequality relating m∠1 to m∠2.
15. Write an inequality relating AB to DE.
16. Write an inequality about the length of GH .
17. 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. ____________________________________
For numbers 18 – 20, decide if the statement is Always, Sometimes, or Never true.
18. If a median of a triangle is also an altitude of the triangle, the triangle is scalene.
19. A median of a triangle bisects the side to which it is drawn.
20. If a median of a triangle is also an altitude, then it is also an angle bisector.
21. The sides of an isosceles triangle are whole numbers. If the perimeter is 24, how many different triangles are possible?
Write out all possible values of the sides and determine which will form a triangle.
10
For problems 22 – 24, refer to the information below.
Given: ∆ABC, A(–2, –3), B(2, 8), and C(8, 6)
8
6
22. Find the equation of the altitude to BC.
4
2
23. If BD is a median, what are the coordinates of D?
-10 -8
-6
-4
-2
2
4
6
8
10
-2
24. What is the equation of the median, BD.
-4
-6
-8
-10
25. Write a valid inequality of the restrictions on x.
(5x – 10)°
20°
26. The vertices of ∆ABC are A(4, 0), B(–2, 4), and C(0, 6). Find the coordinates of the orthocenter of ∆ABC.
10
8
6
4
2
-10 -8
-6
-4
-2
2
-2
-4
-6
-8
-10
27. The vertices of ∆XYZ are X(0, 4), Y(6, 12), and Z(12, 2). Find the coordinates of the centroid of ∆XYZ.
4
6
8
10
28. Write a valid inequality of the restrictions on x.
(5x – 10)°
29. The perpendicular bisectors of ∆ABC meet at point G. Find GC.
AD = 24, BG = 25, GH = 7.
(2x)°
A
24
D
C
G
R
7
25
H
B
30. The angle bisectors of ∆ABC meet at point G. Find GD.
AD = 12, BG = 15, GH = 9.
A
12
D
C
G
R
9
15
H
B
31. P is the circumcenter of ∆XYZ. Find PZ.
SX = 3, SP = 4, RZ = 12.
X
3
S
R
4
P
12
Y
32. P is the incenter of ∆XYZ and ZP = 15, XN = 24, and XP = 26. Find PO.
Z
X
M
26
24
P
Y
N
15
O
Z
Use the following information for numbers 33 – 37: L is the centroid of ∆MNO, NP = 14, ML = 20, and NL = 9.
33. PO = ? .
M
34. MP =
? .
R
35. NQ =
? .
36. LQ =
? .
37. Perimeter of ∆NLP
20
Q
L
9
N
? .
14
P
O