Triangle Proofs

B

A

ED

C

J

E

T

M

State the reason for each statement:

JE

T

M

Given: E is the midpoint of MJ. TE MJ.

Prove: MET JET

Statements:1. E is the midpoint of MJ

2. ME JE

3. TE MJ

4. MET JET

5. TE TE

6. ∆MET ∆JET

Reasons:1. Given2. Def. of midpoint.3. Given4. If 2 lines are , then they form

adjacent angles.5. Reflexive Property6. SAS Congruence Theorem

State the reason for each statement:

Statements:1. BD BC

2. AD ║ EC

3. D C4. ABD EBC

5. ∆ABD ∆EBC

B

A

ED

C

Reasons:1. Given2. Given3. Alternate Interior Angles4. Vertical Angles Theorem5. ASA Congruence Theorem

Given: AD ║EC BD BCProve: ∆ABD ∆EBC

Prove ∆PQR ∆RSP

Statements:1.

2.

3.

4.

Reasons:1.

2.

3.

4.

Given: QP RS and QP = RSProve: ∆PQR is congruent to ∆RSP

Prove ∆ABD ∆ACD

Statements:1.

2.

3.

4.

Reasons:1.

2.

3.

4.

Given: Prove: ∆ABD is congruent to ∆ACD

Prove ∆ABC ∆DEC … are they?

Statements:

1.

2.

3.

4.

5.

Reasons:

1.

2.

3.

4.

5. What is the problem here??

Given: Prove: ∆ABC is congruent to ∆DEC