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Math Help - Triangle Congruence Postulates -- Check please?

  1. #1
    Junior Member StonerPenguin's Avatar
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    Triangle Congruence Postulates -- Check please?

    Hello again! Still working on my sister's geometry homework (it's complicated -- She's gotta work on literature exams, so I'm doing all of her geometry stuff. I finished geometry with nearly perfect grades a few years ago but I've forgotten quite a bit!) Without further ado, here's the question: [It's a 'fill-in-the-blank' type question. My answers will be underlined and in blue.]

    7-11: Using the diagram below and the given information, complete the following statements by writing one of the following:
    AAS    ASA   HL   SAS   SSS




    7. If \overline{AB} \overline{CB} and \overline{BD} bisects ∠ABC, then ΔABD ΔCBD by SAS

    8. If ∠ADB ≅ ∠CDB and A C, then ΔABD ΔCBD by ASA

    9. \overline{BD} is an altitude and \overline{AB} \overline{CB}, then ΔABD ΔCBD by SSS. Then ∠A ∠C because Corresponding parts of ≅ Δs are ≅.

    10. If ∠ADB ≅ ∠CDB and \overline{BD} \overline{AC}, then ΔABD ΔCBD by AAS

    11. If \overline{AB} \overline{CB} and \overline{BD} bisects \overline{AC}, then ΔABD ΔCBD by HL.
    And ∠ADB ≅ ∠CDB since Corresponding parts of ≅ Δs are ≅, so \overline{BD} \overline{AC} by Theorem 3.8 [If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.]

    I have a horrible feeling I got this abysmally wrong...
    As always, any help or explanation would be appreciated!
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  2. #2
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    Re: Triangle Congruence Postulates -- Check please?

    isn't she just going to fail her geometry tests?

    7) is correct

    8) is incorrect
    Spoiler:
    AAS


    9) is incorrect
    Spoiler:
    I'm guessing because they use the word altitude here they are looking for HL (which I assume means height, leg), further you can't directly say that AD = CD


    10) is correct

    11) is incorrect
    Spoiler:
    SSS
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  3. #3
    Junior Member StonerPenguin's Avatar
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    Re: Triangle Congruence Postulates -- Check please?

    Wow, I did poorly on that! Thank you. And, no she won't fail any tests (other than the SAT maybe :P). She's homeschooled, we're doing a correspondence course (sent through the mail). She's getting extremely close to her deadline, she has to finish American Literature, British Literature, World History, French I & II and Geometry before May or she'll fail (which would be a big waste of money). It's not a situation I'm proud of but things are the way they are. Believe me, I don't want to do her homework Just gotta power through this so I can get back to learning JavaScript

    Anyway, if you are alright with helping me, I'll keep all my questions in one thread. I'm still pretty good at plug-and-chug Geometry but I'm bad at proof stuff. So that's what I'll need help with but I promise I will always make an attempt to answer before requesting help/double-checking. So here's another proof question. Again, fill-in-the-blank. My answers will be in blue.

    Finish the proof that \overline{BC} \overline{DE} by filling in the missing statements and reasons.



    Statements Reasons
    1. \overline{AB} \overline{AD} 1. Given
    2. ∠BAC ≅ ∠DAE 2. Reflexive [because ∠A = ∠A right?]
    3. \overline{AC} \overline{AE} 3. Given
    4. ΔEAD ≅ ΔCAB 4. SAS
    5. \overline{BC} \overline{DE} 5. Corresponding parts of ≅ Δs are ≅.

    **Statement 1 is a question/blank -- I can't make overlined text blue.**
    How was that? Thank you as always.
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    Re: Triangle Congruence Postulates -- Check please?

    this all looks fine
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  5. #5
    Junior Member StonerPenguin's Avatar
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    Re: Triangle Congruence Postulates -- Check please?

    Alright I only have two or three more proofs to do then I should be able to go a good long while without any assistance. Thanks for checking over my work, I'm just not too confident since I'm rushing through this.
    Here we go again!
    Prove that \overline{AC} \overline{BD} (Not a fill in the blank, gotta come up with all the reasons and statements)

    Statements Reasons
    ∠ABC ≅ ∠BAD Given
    \overline{AB} \overline{AB} Reflexive Property of segment congruence
    ∠BAC ≅ ∠ABD Given
    ΔBAC ≅ ΔABD ASA
    \overline{AC} \overline{BD} Corresponding parts of ≅ Δs are ≅

    Oh hey, that was pretty easy. I guess I didn't need help with that after all
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  6. #6
    Junior Member StonerPenguin's Avatar
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    Re: Triangle Congruence Postulates -- Check please?

    Howdy, this should be the last proof I'll need help with for a while Fill-in-the-blank, my answers are in blue.

    Based on the diagram, finish the following proof that \overline{AD} \overline{CD}



    Statements Reasons
    1. \overline{AC} \overline{BD} 1. Given
    2. ∠AEB and ∠CEB are right angles 2. Given
    3. ΔAEB and ΔCEB are right Δs 3. Definition of Right triangles
    4. \overline{AB} \overline{BC} 4. Given
    5. \overline{BE} \overline{BE} 5. Reflexive Property of Segment Congruence
    6. ΔABE ≅ ΔCBE 6. Hypotenuse-Leg Congruence Theorem
    7. \overline{AE} \overline{CE} 7. Corresponding parts of ≅ Δs are ≅
    8. \overline{AC} \overline{DE} [I'm kinda confused by this, but \overline{AC} \overline{BD} has already been stated.] 8. Definition of Perpendicular lines
    9. ΔAED and ΔCED are right Δs 9. Definition of a Right Triangle
    10. \overline{DE} \overline{DE} 10. Reflexive Property of Segment Congruence
    11. ΔAEB≅ ΔCEB 11. Leg-Leg Congruence Theorem
    12. \overline{AD} \overline{CD}
    12. Corresponding parts of ≅ Δs are ≅

    I'm not completely sure I did that right....
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    Re: Triangle Congruence Postulates -- Check please?

    Quote Originally Posted by StonerPenguin View Post
    Howdy, this should be the last proof I'll need help with for a while Fill-in-the-blank, my answers are in blue.

    Based on the diagram, finish the following proof that \overline{AD} \overline{CD}



    Statements Reasons
    1. \overline{AC} \overline{BD} 1. Given
    2. ∠AEB and ∠CEB are right angles 2. Given
    3. ΔAEB and ΔCEB are right Δs 3. Definition of Right triangles
    4. \overline{AB} \overline{BC} 4. Given
    5. \overline{BE} \overline{BE} 5. Reflexive Property of Segment Congruence
    6. ΔABE ≅ ΔCBE 6. Hypotenuse-Leg Congruence Theorem
    7. \overline{AE} \overline{CE} 7. Corresponding parts of ≅ Δs are ≅
    8. \overline{AC} \overline{DE} [I'm kinda confused by this, but \overline{AC} \overline{BD} has already been stated.] 8. Definition of Perpendicular lines
    9. ΔAED and ΔCED are right Δs 9. Definition of a Right Triangle
    10. \overline{DE} \overline{DE} 10. Reflexive Property of Segment Congruence
    11. ΔAEB≅ ΔCEB 11. Leg-Leg Congruence Theorem
    12. \overline{AD} \overline{CD}
    12. Corresponding parts of ≅ Δs are ≅

    I'm not completely sure I did that right....
    for 11 I think you mean AED and CED otherwise looks lok
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