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Geometry
Triangle Congruence Proofs – SSS, SAS
1)
Given: M ≅ PO and MO ≅ P
M
Prove: ∆MO ≅ ∆PO
O
Proof:
M ≅ PO
Given
P
MO ≅ P
Given
O ≅ O
___________________________________
∆MO ≅ ∆PO
___________________________________
2) AC ≅ DC and BC ≅ CE. Write a paragraph proof to show that ∆ABC ≅ ∆DEC
B
C
D
A
E
3)
Given: AB ≅ CB, AD ≅ CD
Prove: ∆ABD ≅ ∆CBD
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4)
Given: RE ≅ CA, RD ≅ CT , ∠R ≅ ∠T
R
E
C
A
Prove: ∆RED ≅ ∆CAT
D
5)
T
Given: AB ≅ CD, AF ≅ DE , ∠A ≅ ∠D
Prove: ∆FAC ≅ ∆EDB
E
C
A
B
D
F
Decide whether you can use SSS or SAS Postulate to prove that the triangles below are congruent. If so a) write
the congruence statement and b) identify the postulate. If not, write not possible.
6) Given: A ≅ RW , G ≅ TW , ∠ ≅ ∠W
A
G R
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7)
T
W
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Supply the reasons for the proof below.
8)
A
Given: M is the midpoint AG and of R
Prove: ∆AM ≅ ∆GRM
M
1
2
R
1. ∠1 ≅ ∠2
2. M is the midpoint of AG
G
3. AM ≅ GM
4. M is the midpoint of R
5. M ≅ RM
6. ∆AM ≅ ∆GRM
Write a two Column Proof.
B
9)
Given: AE and BD bisect each other
Prove: ∆ACB ≅ ∆ECD
C
D
A
E
10)
Given: K bisects ∠JM , J ≅ M
J
Prove: ∆JK ≅ ∆MK
K
M
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Answer Key
1) Reflexive Property of Congruence, SSS
2) ∠ACB ≅ ∠DCE because they are vertical angles. ∆ABC ≅ ∆DEC by SAS
3)
AB ≅ CB
Given
AD ≅ CD
Given
Reflexive
∆ABD ≅ ∆CBD SSS
BD ≅ BD
4) Not enough information. Angle t is not included between the congruent sides. Triangles may or may not be
congruent.
AF ≅ DE , Given; ∠A ≅ ∠D, Given; AB ≅ CD, Given
5)
AB = CD, def. congruent segments; AB + BC = CD + BC , Addition Prop. of Equality
AC = BD, Segment Addition Postulate; AC ≅ BD def. of congruent segments
∆FAC ≅ ∆EDB SAS
6) a. ∆AG ≅ ∆RWT b. SAS
7) Not enough information
8) 1) Vertical Angles, 2) Given, 3) Def. of midpoint, 4) Given, 5) Def. of midpoint, 6) SAS
AE & BD bisect each other, Given
AC ≅ EC , Def. Segment Bisector
9) BC ≅ DC , Def. Segment Bisector
∠ACB ≅ ∠ECD, Vertical Angles are congruent
∆ACB ≅ ∆ECD SAS
K bisects ∠JNM, Given
∠JK ≅ ∠MK , Def. Angle Bisector
10)
J ≅ M , Given
K ≅ K , Reflexive
∆JK ≅ ∆MK , SAS
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