# Math Help - Triangle Congruence Postulates -- Check please?

1. ## 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!

2. ## 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

3. ## 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. img.top {vertical-align:15%;} $\overline{AB}$ ≅ img.top {vertical-align:15%;} $\overline{AD}$ 1. Given 2. ∠BAC ≅ ∠DAE 2. Reflexive [because ∠A = ∠A right?] 3. img.top {vertical-align:15%;} $\overline{AC}$ ≅ img.top {vertical-align:15%;} $\overline{AE}$ 3. Given 4. ΔEAD ≅ ΔCAB 4. SAS 5. img.top {vertical-align:15%;} $\overline{BC}$ ≅ img.top {vertical-align:15%;} $\overline{DE}$ 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.

4. ## Re: Triangle Congruence Postulates -- Check please?

this all looks fine

5. ## 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 img.top {vertical-align:15%;} $\overline{AB}$ ≅ img.top {vertical-align:15%;} $\overline{AB}$ Reflexive Property of segment congruence ∠BAC ≅ ∠ABD Given ΔBAC ≅ ΔABD ASA img.top {vertical-align:15%;} $\overline{AC}$ ≅ img.top {vertical-align:15%;} $\overline{BD}$ Corresponding parts of ≅ Δs are ≅

Oh hey, that was pretty easy. I guess I didn't need help with that after all

6. ## 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. img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{BD}$ 1. Given 2. ∠AEB and ∠CEB are right angles 2. Given 3. ΔAEB and ΔCEB are right Δs 3. Definition of Right triangles 4. img.top {vertical-align:15%;} $\overline{AB}$ ≅ img.top {vertical-align:15%;} $\overline{BC}$ 4. Given 5. img.top {vertical-align:15%;} $\overline{BE}$ ≅ img.top {vertical-align:15%;} $\overline{BE}$ 5. Reflexive Property of Segment Congruence 6. ΔABE ≅ ΔCBE 6. Hypotenuse-Leg Congruence Theorem 7. img.top {vertical-align:15%;} $\overline{AE}$ ≅ img.top {vertical-align:15%;} $\overline{CE}$ 7. Corresponding parts of ≅ Δs are ≅ 8. img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{DE}$ [I'm kinda confused by this, but img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{BD}$ has already been stated.] 8. Definition of Perpendicular lines 9. ΔAED and ΔCED are right Δs 9. Definition of a Right Triangle 10. img.top {vertical-align:15%;} $\overline{DE}$ ≅ img.top {vertical-align:15%;} $\overline{DE}$ 10. Reflexive Property of Segment Congruence 11. ΔAEB≅ ΔCEB 11. Leg-Leg Congruence Theorem 12. img.top {vertical-align:15%;} $\overline{AD}$ ≅ img.top {vertical-align:15%;} $\overline{CD}$ 12. Corresponding parts of ≅ Δs are ≅

I'm not completely sure I did that right....

7. ## Re: Triangle Congruence Postulates -- Check please?

Originally Posted by StonerPenguin
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. img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{BD}$ 1. Given 2. ∠AEB and ∠CEB are right angles 2. Given 3. ΔAEB and ΔCEB are right Δs 3. Definition of Right triangles 4. img.top {vertical-align:15%;} $\overline{AB}$ ≅ img.top {vertical-align:15%;} $\overline{BC}$ 4. Given 5. img.top {vertical-align:15%;} $\overline{BE}$ ≅ img.top {vertical-align:15%;} $\overline{BE}$ 5. Reflexive Property of Segment Congruence 6. ΔABE ≅ ΔCBE 6. Hypotenuse-Leg Congruence Theorem 7. img.top {vertical-align:15%;} $\overline{AE}$ ≅ img.top {vertical-align:15%;} $\overline{CE}$ 7. Corresponding parts of ≅ Δs are ≅ 8. img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{DE}$ [I'm kinda confused by this, but img.top {vertical-align:15%;} $\overline{AC}$ ┴ img.top {vertical-align:15%;} $\overline{BD}$ has already been stated.] 8. Definition of Perpendicular lines 9. ΔAED and ΔCED are right Δs 9. Definition of a Right Triangle 10. img.top {vertical-align:15%;} $\overline{DE}$ ≅ img.top {vertical-align:15%;} $\overline{DE}$ 10. Reflexive Property of Segment Congruence 11. ΔAEB≅ ΔCEB 11. Leg-Leg Congruence Theorem 12. img.top {vertical-align:15%;} $\overline{AD}$ ≅ img.top {vertical-align:15%;} $\overline{CD}$ 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