Name: ____________KEY_________________
CP Geometry
Chapter 6 Review
1.
Find the measure of the largest angle of a triangle is the measures of its interior angles are in the
ratio 3:5:7.
2.
ANS: ______84°__________
Find the measure of the vertex angle of an isosceles triangle if the measures of the vertex angle
and a base angle have the ratio 4:3.
3.
ANS: ______72°__________
The measures of a pair of consecutive angles of a parallelogram have the ratio 5:7. Find the
measure of each angle of the parallelogram.
4.
Solve for x.
ANS: ____75°, 105°______
5.
a.
2 8
 x = 24
6 x
d.
4
1

x=5
x 3 x 3
b.
2 x

x = ±10
x 50
e.
3 x4

x
7
c.
2x  5 9

x = 5.875
3
4
x = 7, -3
If KW EG , find the length of the indicated segments.
E
a. HE = 20, KE = 12, WG = 9, HG = __15____
K
b. KH = 7, KE = 14, HG = 12, HW = ___4______
c. HW = 4, WG = 12, HE = 28, KH = __7_______
G
W
d. KH = 9, KE = 12, HG = 42, WG = ___24______
e. KH = 2x - 15, KE = x, HW = 1, HG = 4. Find KH and KE. ____3; 9_____________
6.
7.
8.
SHE . Name three pairs of congruent angles and three equal ratios.
GA AL GL


_____ G  S ; A  H ; L  E ;
_______________________________
SH HE SE
The ratio of two similar polygons is 3:5. If the length of the shortest side of the smaller polygon
is 24, find the length of the shortest side of the larger polygon. ____40___________
GAL
ZAP MYX . If ZA = 3, AP = 12, ZP = 21 and YX = 20, find the lengths of the remaining
sides of MYX .
___MY = 5; MX = 35_____________________
H
9.
Quadrilateral ABCD is similar to quadrilateral RSTW. The lengths of the sides of quadrilateral
ABCD are 3, 6, 9, and 15. If the length of the longest side of quadrilateral RSTW is 20, find the
perimeter of RSTW. ______ 44_______________
10.
RST JKL
a. RA and JB are medians to sides ST and KL , respectively. RS = 10 and JK = 15. If the length
of JB exceeds the length of RA by 4, find the length of medians JB and RA . RA = 8; JB = 12
b. SH and KO are altitudes to sides RT and JL , respectively. If SH = 12, KO = 15, LK = 3x -2,
and TS = 2x + 1, find the lengths of LK and TS . __ LK = 17.5; TS = 14____
c. The perimeter of RST is 25 and the perimeter of JKL is 40. If ST = 3x + 1 and
KL = 4x + 4, find the lengths of ST and KL . ____ ST = 10; KL = 16____
d. The ratio of RST to JKL is 3:x. The length of altitude SU is x - 4 and the length of altitude
KV is 15. Find the length of altitude SU . _____ 5_______
Given: XW = XY, HA  WY , KB  WY
Prove: HWA KYB
11.
Statement
1. XW = XY,
HA  WY , KB  WY
2. W  Y
HAW , KBY are rt.
3.
4. HAW  KBY
5. HWA KYB
X
K
H
W
12.
A
Given: EF is the midsegment of
Prove: (EI)(CG) = (CI)(EF)
ABC
F
I
13.
C
G
Statement
Given: HW ‌ TA
W
HY AX
T
H
Prove:
Statement
1. EF is midsegment ABC
2. EF AC
3.
FEI  GCI
4. EIF  CIG
5. EIF CIG
EI
CI

6.
EF CG
7. (EI)(CG) = (CI)(EF)
B
A
2.
3.
4.
5.
BAT
Def. of  lines
Rt. angles are 
AA Sim. Post.
Y
B
E
Reason
1. Given
A
AX
AT

HY HW
X
Y
1. HW ‌ TA ; HY ‌ AX
2. W  ATX ; Y  AXT
3.
AXT HYW
AX
AT

4.
HY HW
Reason
1. Given
2. Def. of midsegment
3.
4.
5.
6.
PAI
VAT
AA Sim. Post.
CSSTP
7. Cross Prod. =
Reason
1. Given
2. PAI
3. AA Sim. Post.
4. CSSTP