# Thread: Givens. Statements, proofs

1. ## Givens. Statements, proofs

Given: RA bisects ∠TRI; ∠TAR≅∠IAR
Prove: ∠T≅∠I
Statement:
1. RA bisects ∠TRI
2. ∠TRA≅∠IRA
3. ∠TAR≅∠IAR
4. RA≅RA
5.ΔTAR≅ΔIAR
6. ∠T≅∠I

Choose the best answer.

A)1. Given; 2. Definition of midpoint of a segment; 3. Given; 4. Symmetric property; 5. SSS postulate; 6. CPCTC

B)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Commutative property; 5. AAA postulate; 6. CPCTC

C)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Reflexive property; 5. ASA postulate; 6. CPCTC

Can someone help please?

2. Originally Posted by tysonrss
Given: RA bisects ∠TRI; ∠TAR≅∠IAR
Prove: ∠T≅∠I
Statement:
1. RA bisects ∠TRI ===== Given
2. ∠TRA≅∠IRA ======= Definition of an angle bisector
3. ∠TAR≅∠IAR ======= Given
4. RA≅RA =========== Reflexive property
5.ΔTAR≅ΔIAR ======== ASA postulate
6. ∠T≅∠I ========== CPCTC

Choose the best answer.

A)1. Given; 2. Definition of midpoint of a segment; 3. Given; 4. Symmetric property; 5. SSS postulate; 6. CPCTC

B)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Commutative property; 5. AAA postulate; 6. CPCTC

C)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Reflexive property; 5. ASA postulate; 6. CPCTC
Can someone help please?
There you go!

3. Originally Posted by tysonrss
...
Choose the best answer.

A)1. Given; 2. Definition of midpoint of a segment; 3. Given; 4. Symmetric property; 5. SSS postulate; 6. CPCTC

B)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Commutative property; 5. AAA postulate; 6. CPCTC

C)1. Given; 2. Definition of an angle bisector; 3. Given; 4. Reflexive property; 5. ASA postulate; 6. CPCTC

Can someone help please?
Obviously masters has provided the correct answer. Where did you have trouble in this problem? Comparing A, B and C, we see that they differ in statements 2, 4, and 5. "Definition of a midpoint" should have raised a red flag or two, since this given info is about an ANGLE bisector.
"SSS" is terribly wrong because in the preceding statements, three sides were not mentioned.
"AAA" is wrong for the same reason... two angle and a side (the included side) were mentioned, not three angles.

Also, knowing what symmetry and commutative properties look like would immediately rule those out as justification for statement 4.

4. Thanks you guys.