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Geometry
Chapter 5 Review
Name:KEY Date:_________ Period: ___
Find the value of x.
1.
2.
2(x+5)=3x-9
2(x+5)=3x
X=10
X=10
4.
3. 6x+4=8x-6
3x=5x-9
X=4.5
X=5
Use the figure at the right for Exercises 5–7.
5. Is AQ a perpendicular bisector or an altitude? altitude
6. Is RB a median or an angle bisector? Angle bisector
7. What kind of segment is CP ?median
In ∆DEF, M is the centroid.
8. Find MK and DK.
MK=4, DK=12
9. Find LM and LE. LM=3, LE=9
10. If MJ is 4, then find the value of x and y. 2y = 4
Y=2
2x = 8
x=4
11. In ∆ABC, G is the midpoint of AB, H is the midpoint of BC, and I is the midpoint of AC. What are the three pairs
of parallel segments? Explain.
12. Suppose EP = PG. Explain how you can find mPQG.
85 because corresponding angles of parallel lines are equal.
Find the value of x and y.
13.
14.
3 equal sides gives 3 equal angles
So 180/3 equal 60 for each angle
X + 20 = 60 4y = 60
X = 40
y = 15
15.
3 equal angles gives 3 equal sides
so each side = 24
2x = 24 3y = 24
x = 12
y=8
16.
X = 62 y = 59
y= 65
x = 50
List the angles of ΔPQR from smallest to largest.
17.
18.
Angle P, R, Q
Angle Q, P, R
List the sides of ΔDEF from shortest to longest.
19.
20.
Angle F = 60
EF, ED, DF
Angle F = 46
EF, DE, DF
For problems 21-24 determine whether the given measures can be the lengths of the sides of a triangle. Write Yes or
No and Explain.
21) 4, 16, 8
No 12 < 16
22) 7, 12, 8
yes 15 > 12
23) 6, 7, 13
no 13 = 13
24) 1, 2, 3
no 3 = 3
For problems 25 - 27, find the range of possible measures for the third side of a triangle given the measures of two
sides. Write answer as a compound inequality.
25) 21 and 22
1 < x < 43
26) 2 and 7
5<x<9
27) 12 and 8
4 < x < 20
28. Given triangle PQR with <P = 29+9n, <Q = 2+10n, and <R = 93 - 5n. List the sides in order from greatest to least.
124 + 14n = 180
14n = 56
n=4
P=65 Q=42 R=73
PQ, QR, RP