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Proofs HW Packet

1. The document provides 10 geometry proofs involving triangle congruence. Each proof lists given information and statements to prove why two triangles are congruent based on that information using angle-angle-side or side-side-side postulates. 2. The proofs utilize various triangle congruence theorems including CPCTC, vertical angles, alternate interior angles of parallel lines, perpendicular bisectors, and midpoints. 3. The final section provides 8 additional mixed proofs for the student to complete.

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Pinky Maligaya Jalamanan
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655 views5 pages

Proofs HW Packet

1. The document provides 10 geometry proofs involving triangle congruence. Each proof lists given information and statements to prove why two triangles are congruent based on that information using angle-angle-side or side-side-side postulates. 2. The proofs utilize various triangle congruence theorems including CPCTC, vertical angles, alternate interior angles of parallel lines, perpendicular bisectors, and midpoints. 3. The final section provides 8 additional mixed proofs for the student to complete.

Uploaded by

Pinky Maligaya Jalamanan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Geometry/Trig Name __________________________

Unit 4 Proving Triangles Congruent Packet Date ___________________________

#1 F
H
Given: LF || WH; HY  LY
Prove: ΔWHY  ΔFLY Y
W L

Statements Reasons

#2 M A

Given: MH || AT; MH  AT
Prove: ΔMAH  ΔTHA
H T
Statements Reasons

#3 W
Given: ZX bisects WZY
ZX bisects WXY Z X

Prove: ΔZYX  ΔZWX


Y
Statements Reasons
#4 A
C
Given: E is the midpoint of AD E
E is the midpoint of BC

Prove: ΔAEB  ΔDEC B


D

Statements Reasons

1. _________________________________ 1. __________________________________
2. _________________________________ 2. __________________________________
3. _________________________________ 3. Given
4. _________________________________ 4. __________________________________
5. _________________________________ 5. Vertical Angles are Congruent
6. _________________________________ 6. __________________________________

#5 A
Given: AC  BD
B  D
Prove: ΔACB  ΔACD B D
C
Statements Reasons

#6 M
Given: MO  NP
MN  MP
Prove: ΔMON  ΔMOP
N P
O

Statements Reasons

1. _________________________________ 1. __________________________________
2. _________________________________ 2. Definition of Perpendicular Lines
3. _________________________________ 3. __________________________________
4. _________________________________ 4. Given
5. _________________________________ 5. __________________________________
6. _________________________________ 6. __________________________________
#7 W Z
Given: WO  ZO; XO  YO
Prove: W  Z O

X Y
Statements Reasons

#8 Q

Given: PR bisects QPS and QRS R P

Prove: RQ  RS
S
Statements Reasons

#9 A

Given: AC  BD; AD  DC B D

Prove: AB  BC
C
Statements Reasons
#10 Y Z
2
Given: ZW || YX; ZW  XY 3
Prove: ZY || WX 4
1
X W
Statements Reasons

1. _________________________________ 1. _________________________________
2. _________________________________ 2. If lines are parallel, then alternate interior
angles are congruent.

3. _________________________________ 3. _________________________________
4. _________________________________ 4. _________________________________
5. ΔXYZ  ΔZWX 5. _________________________________
6. _________________________________ 6. CPCTC
7. _________________________________ 7. _________________________________
_________________________________

S
#11
Given: P  S
O is the midpoint of PS Q
O R
Prove: O is the midpoint of RQ

P
Statements Reasons

1. P  S, O is the midpoint of PS 1. __________________________________


2. __________________________________ 2. __________________________________
3. __________________________________ 3. Vertical Angles are Congruent
4. __________________________________ 4. __________________________________
5. RO  QO 5. __________________________________
6. __________________________________ 6. __________________________________

#12 J

Given: JK  KM, JL  ML
K L
Prove: KL bisects JKM

Statements M Reasons

1. JK  KM, JL  ML 1. __________________________________
2. __________________________________ 2. __________________________________
3. __________________________________ 3. __________________________________
4. __________________________________ 4. CPCTC
5. __________________________________ 5. __________________________________
Mixed Proofs Practice

Directions: Complete the proofs on a separate piece of paper. Mark diagrams as necessary.

1) Given: AB || DE; AB  ED 2) Given: AB || CD; AD || CB


Prove: ΔABC  ΔCDA
Prove: ΔABM  ΔEDM
B C
A B 4
3
M
2
1
D E A D

3) Given: MO bisects LMN 4) Given: X and Y are right angles;


L and N are right angles XZ  YZ
M W
Prove: ΔLMO  ΔNMO Prove: ΔWXZ  ΔWYZ

L N X Y

O Z

5) Given: C is the midpoint of AE 6) Given: AB  CB, AD  CD

C is the midpoint of BD Prove: A  C


B
Prove: AB || ED
A B

D
D E A C

7) Given: MT bisects ATH, AT  HT 8) Given: BC || AD, A  C


Prove: BC  AD
Prove: MT bisects AMH
B C
A

M T

H A D

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