Download Proving Congruent Triangles

Proving Congruent Triangles
Side-Side-Side Postulate (SSS) - If the sides of one triangle are congruent to the sides of a second triangle, then
the triangles are congruent.
B
A
E
C
D
F
Side-Angle-Side Postulate (SAS) - If two sides and the included angle of one triangle are congruent to two sides and the
included angle of another triangle, then the triangles are congruent.
B
A
E
C
D
F
Angle-Side-Angle Postulate (ASA) - If two angles and the included side of one triangle are congruent to two angles and the
included side of another triangle, then the triangles are congruent.
B
A
E
C
D
F
Angle-Angle-Side Theorem (AAS) - If two angles and a nonincluded side of one triangle are congruent to the
corresponding two angles and side of a second triangle, then the triangles are congruent.
B
A
E
C
D
F
C.P.C.T.C. - Corresponding Parts of Congruent Triangles are Congruent
Directions: Write a proof for each.
1. Given: (D ≅ (E
D B
C is the midpoint of DE
C
Prove: + DBC ≅+ EAC
A
Statement
1. (D ≅ (E
E
Reason
1. Given
C is the midpoint of DE
D 2. Given: DE bisects BA
BA bisects DE
C
Prove: + DBC ≅+ EAC
A
Statement
1. DE bisects BA
BA bisects DE
B
Reason
1. Given
E
3. Given: + ABC is an isosceles triangle with vertex (ABC
B
D is the midpoint of AC
Prove: + ABD ≅+CBD
A
Statement
1. + ABC is an isosceles triangle with vertex (ABC
D
C
Reason
1. Given
D is the midpoint of AC
4. Given: BD ⊥ AC
B
BD bisects AC
Prove: + ABD ≅+CBD
A
Statement
1. BD ⊥ AC
BD bisects AC
Reason
1. Given
D
C
5. Given: AB & DC
A
B
BC & AD
Prove: (A ≅ (C
D
Statement
1. AB & DC
C
Reason
1. Given
BC & AD
6. Given: (ADB ≅ (CBD
A
B
DA ≅ BC
Prove: AB ≅ CD
D
Statement
1. (ADB ≅ (CBD
DA ≅ BC
Reason
1. Given
C
7. Given: (BDE ≅ (BED
(A ≅ (C
B
AD ≅ CE
Prove: + BAE ≅+ BCD
A
Statement
1. (BDE ≅ (BED
(A ≅ (C
D
E
C
Reason
1. Given
AD ≅ CE
8. Given: (ABE ≅ (CBD
(A ≅ (C
B
AB ≅ CB
Prove: + ABD ≅+CBE
A
Statement
1. (ABE ≅ (CBD
(A ≅ (C
AB ≅ CB
Reason
1. Given
D
E
C
9. Given: (ABD ≅ (CBE
B
(A ≅ (C
AB ≅ CB
Prove: AE ≅ CD
A
Statement
1. (ABD ≅ (CBE
(A ≅ (C
D
E
C
Reason
1. Given
AB ≅ CB
B
10. Given: AE ≅ CD
(A ≅ (C
AB ≅ CB
Prove: DB ≅ EB
A
Statement
1. AE ≅ CD
(A ≅ (C
AB ≅ CB
Reason
1. Given
D
E
C
B
11. Given: + ABC is an isosceles triangle with base AC
(BDE ≅ (BED
(A ≅ (C
Prove: + ABE ≅+CBD
A
Statement
1. + ABC is an isosceles triangle with base AC
(BDE ≅ (BED
D
E
C
Reason
1. Given
(A ≅ (C
12. Given: (ABE ≅ (DCE
B
C
(EAD ≅ (EDA
E
Prove: BA ≅ CD
A
Statement
1. (ABE ≅ (DCE
(EAD ≅ (EDA
Reason
1. Given
D
13. Given: (A ≅ (ABE
B
C
(ECD ≅ (D
(A ≅ (D
AE ≅ DE
A
D
Prove: + BEC is an isosceles triangle
E
Statement
1. (A ≅ (ABE
(ECD ≅ (D
(A ≅ (D
AE ≅ DE
Reason
1. Given