D E F 4 5 9 7 C B A Q R B A R A T X E Honors Geometry Name Chapter 8 Problems 1) ~ ABC EFD Find DF and AB. 2) ~ STP RUN , 12 SP , 8 ST , 11 TP , 36 RU Find UN and RN. 3) Given: AB RB QB AR Prove: All three triangles in the figure are similar. Statements Reasons 4) Given: TA bisects ETR AT EX AR RT Prove: ~ ART ETX Statements Reasons
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Honors Geometry Name Chapter 8 Problems 1) ~ABC EFD Find DF and AB. 2) ~STP RUN , 12SP , 8ST , 11TP , 36RU Find UN and RN.
3) Given: AB RB
QB AR
Prove: All three triangles in the figure are similar. Statements Reasons
4) Given: TA bisects ETR
AT EX
AR RT Prove: ~ART ETX Statements Reasons
EWR
Q
S
X
P
TW
M
R
C
A
T
RNS
F
M
5) Given: PQRS
Prove: PXS EXW Statements Reasons
6) Given: RT MT
AM MT AMC AWM Prove: MCW AMW Statements Reasons
7) Given: FN MR
NT MS
Prove: SFN NTR Statements Reasons
CS
ZPD
B
R
Y
AW E
N
F
ED
C
BA
8) Given: D S B C 20BP
21PD 11SZ 11.5SC Find: CZ and BD
9) Given: E Y
W R 3NW x 6AY
4AR x 9NE The Perimeter of 27NEW Find: YR, NW, RA and WE
Determine the ratio of the perimeter of NEW to the perimeter of AYR. 10) Given: A E Prove: AC BC EC DC Statements Reasons
Q S
R
P
ED
B
CA
11) Given: RQ PS
PR RS
Prove: 2RQ PQ QS
Statements Reasons
12) Given: AB DB
CE AD Prove: AB ED CE BD Statements Reasons 13) A fence post 5 feet high casts a shadow 6 feet long. the shadow is created by a light on a barn roof. The wall of the barn roof is 20 feet away from the fence post. How high is the light?
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B
A
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W
SP
R P
OM
K
FE
D
C
BA
14) Given: ABC ADB 10AB
4AD Find: AC 15) Given: SPW SWL 4PS 9SL Find: SW
16) Given: KOPR is a rectangle
RM PM 9OM 13RP Find: KR, MR and MP
17) Given: CD AB
AE CB AC BC 13AC 12CD 5AD Find: AF
D C
BA
DC
B
A
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E
D
C B
A
WP
MN
TF
18) Given: DC AB
6DC 10AC DAC CAB CBA Find: AB 19) Given: D CAB 6AB 4BC Find: CD 20) Given: ABCD is a rectangle
DE AC 4CE 16AD Find: DC
21) Given: FT FP
NM FP
PW FP 8FT
4NM Find: PW
C
BD
m
n
P
A
KP
W
N
M
M
KJ
H
G
FE
22) In trapezoid LPST, the diagonals intersect at R. 12LS , 4LR and 3PR . Find PT. 23) Given: m n
A and C m B and D n
AB CD at P 12AC
4BD 48AB Find: AP
24) Given: MP NK
NW MK 10KN 8WK
12MK Find: PK 25) Given: 5JH
4MJ EFGK is a parallelogram Find: EM
QM
N
P
T
S
MN
KJ
F
GOD
TE
P
NA
M
R T
SQ
P
26) Given: ST MT
PQ MT
MN MT 2TQ 6MQ
12MN Find: PQ and ST
27) Given: JK MN
10FJ 8.4FK 16JN 30.2MN Find: JK and KM
28) Given: MN PT DG
12MP 15AE 9EO 36NG Find: PD, NT and TG
29) Given: QS RT
8PQ 4QR 10QS
6PS Find: ST and RT
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B
A
A
C B
E D
MFE
D C
BA
RP
T
Q
30) Given: ABD CBD 10AB 12BC 11AC Find: DC
31) Given: CB DE
3AB 5AC 8CE 10DE Find: BD and BC
32) Given: AB CD
bisectsME AMD
4AE 6ED AM 14AC Find: MB 33) Given: 2PR TR QT PQ QR
Find: PT
GFE
DC
B
A
34) Given: EF AC
bisectsBD ABC
3BE 6AE 2EG 8BF Find: AD, GF, DC and FC 35) A pole stands perpendicular to the ground, 20 feet away from a 30 foot tall light post, and casts a shadow on the ground. When Mr. Herrmann moves the pole 5 feet further away from the light post, the length of the pole's shadow increases by 3 feet. How tall is the pole?
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The Two Pole Problem
First, do these three problems where the given is the same except that the length of CB is changed. Look carefully at your answers and see if you notice anything. In fact, you might try to guess what happens before
you start. Things like, in which case will EF be shortest?
Given: AB CB
DC CB
EF CB 10AB 6DC 1) Given: 20BC Find: EF 2) Given: 40BC Find: EF 3) Given: 100BC Find: EF 4) Considering your answers to these three problems, see if you can formulate a conjecture about “The Two Pole Problem”. Write a formula for EF in terms of just AB and CD.
5) Given: WP PN
KS PN
MN PN 4WP 9MN Find: KS
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L O
The Golden Triangle
Given: GO GL 1OL
GD DO OL 1) Find each of the following angle measures. m G
m L m GOL m DLO m DOL 2) Now look at the triangles and the angle measures and determine the lengths of each of the following. Do not expect integer answers. OL= OG= OD= GL= GD= DL= 3) And finally, determine each of the following ratios,
OL
LD
LD
OL
OL
GO
GO
OL
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