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Math Help - Givens. Statements, proofs

  1. #1
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    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?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by tysonrss View Post
    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!
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  3. #3
    Super Member TheChaz's Avatar
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    Quote Originally Posted by tysonrss View Post
    ...
    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.
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  4. #4
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    Thanks you guys.
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