Download Using Corresponding Parts of Congruent Triangles

Name
Class
4-4
Date
Practice (continued)
Form G
Using Corresponding Parts of Congruent Triangles
5. Complete the proof.
A
B
Given: BD ' AB, BD ' DE, BC > DC
Prove: /A > /E
C
D
Statements
E
Reasons
1) BD ' AB, BD ' DE
1) 9 Given
2) /CDE and /CBA are right angles.
2) Definition of right angles
3) /CDE > /CBA
3) 9 All right angles are congruent.
4) 9 lECD O lACB
4) Vertical angles are congruent.
5) BC > DC
5) 9 Given
6) 9 kCDE O kCBA
6) 9 ASA
7) /A > /E
7) 9 CPCTC
6. Construction Use a construction to prove that the
B
two base angles of an isosceles triangle are congruent.
Given: Isosceles nABC with base AC
Prove: /A > /C
A
Statements
D
C
Reasons
1) nABC is isosceles.
1) 9 Given
2) AB > CB
2) Definition of isosceles triangle.
3) Construct the midpoint of AC
and call it D. Construct DB.
3) Construction
4) 9 AD O CD
4) Definition of midpoint
5) BD > BD
5) 9 Refl. Prop. of Congruence
6) nABD > nCBD
6) 9 SSS
7) 9 lA O lC
7) 9 CPCTC
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Name
Class
4-4
Date
Practice
Form K
Using Corresponding Parts of Congruent Triangles
1. Developing Proof State why the two triangles are
Q
congruent. Then list all other corresponding parts
of the triangles that are congruent.
T
AAS; kQRS O kTWX ; lQ O lT , RS O WX
R
W
S
2. Developing Proof State why nAXY and nCYX are
X
A
C
congruent. Then list all other corresponding parts
of the triangles that are congruent.
B
Answers may vary. Sample: SAS; lAYX O lCXY , AY O CX
X
3. Given: QS 6 RT , /R > /S
Y
Q
Prove: /QTS > /TQR
R
To start, determine how you can prove the triangles are congruent.
The triangles share a side and have a pair of congruent angles.
z
u
Because QS 6 RT , alternate interior angles /SQT and lRTQ
z
S
T
are congruent. The triangles can be proven congruent by AAS.
Statements
Reasons
1) 9 QS 6 RT , lR O lS
1) Given
2) 9 lSQT O lRTQ
2) Alternate interior ' are >.
3) 9 QT O TQ
3) Reflexive Property of Congruence
4) 9 kSTQ O kRQT
4) AAS
5) 9 lQTS O lTQR
5) Corresp. parts of > > are >.
Reasoning Copy and mark the figure to show the given
information. Explain how you would prove AB O DE.
4. Given: AC > DC, /B > /D
AAS and Corresp. parts of O > are O.
A
C
B
B
E
A
C
D
B
C
E
D
E
E
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D
C
D
5. Given: AE bisects BD, DB bisects AE
SAS and Corresp. parts of O > are O.
6. Given: AB 6 DE, AC 5 EC
A
Answers may vary. Sample: AAS and
Corresp. parts of O > are O.
B
A