# CP Geometry Name: ______KEY Chapter 6 Review 1. Find the ```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&deg;__________
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&deg;__________
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&deg;, 105&deg;______
5.
a.
2 8
 x = 24
6 x
d.
4
1

x=5
x 3 x 3
b.
2 x

x = &plusmn;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.
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
```