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

http://i1137.photobucket.com/albums/...exam3Q7-11.png

7. If $\displaystyle \overline{AB}$ **≅**$\displaystyle \overline{CB}$ and $\displaystyle \overline{BD}$ bisects ∠ABC, then ΔABD** ≅** ΔCBD by __SAS__

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

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

10. If ∠ADB **≅ ∠**CDB and $\displaystyle \overline{BD}$ ┴ $\displaystyle \overline{AC}$, then ΔABD** ≅** ΔCBD by __AAS__

11. If $\displaystyle \overline{AB}$ **≅**$\displaystyle \overline{CB}$ and $\displaystyle \overline{BD}$ bisects $\displaystyle \overline{AC}$, then ΔABD** ≅** ΔCBD by __HL__.

And ∠ADB **≅ ∠**CDB since Corresponding parts of ≅ Δs are ≅, so $\displaystyle \overline{BD}$ ┴ $\displaystyle \overline{AC}$ 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!

Re: Triangle Congruence Postulates -- Check please?

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

7) is correct

8) is incorrect

9) is incorrect

10) is correct

11) is incorrect

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 (Wink) Just gotta power through this so I can get back to learning JavaScript :D

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 $\displaystyle \overline{BC}$ ≅ $\displaystyle \overline{DE}$ by filling in the missing statements and reasons.**

http://i1137.photobucket.com/albums/...emexam3Q12.png

**Statements** | **Reasons** |

1. $\displaystyle \overline{AB}$ ≅ $\displaystyle \overline{AD}$ | 1. Given |

2. ∠BAC ≅ ∠DAE | 2. Reflexive [because ∠A = ∠A right?] |

3. $\displaystyle \overline{AC}$ ≅ $\displaystyle \overline{AE}$ | 3. Given |

4. ΔEAD ≅ ΔCAB | 4. SAS |

5. $\displaystyle \overline{BC}$ ≅ $\displaystyle \overline{DE}$ | 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.

Re: Triangle Congruence Postulates -- Check please?

Re: Triangle Congruence Postulates -- Check please?

Alright :D 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 $\displaystyle \overline{AC}$ ≅ $\displaystyle \overline{BD}$ (Not a fill in the blank, gotta come up with all the reasons and statements)

http://i1137.photobucket.com/albums/...emexam4Q14.png

**Statements** | **Reasons** |

∠ABC ≅ ∠BAD | Given |

$\displaystyle \overline{AB}$ ≅ $\displaystyle \overline{AB}$ | Reflexive Property of segment congruence |

∠BAC ≅ ∠ABD | Given |

ΔBAC ≅ ΔABD | ASA |

$\displaystyle \overline{AC}$ ≅ $\displaystyle \overline{BD}$ | Corresponding parts of ≅ Δs are ≅ |

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

Re: Triangle Congruence Postulates -- Check please?

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

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

http://i1137.photobucket.com/albums/...emexam4Q16.png

**Statements** | Reasons |

1. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ | 1. Given |

2. ∠AEB and ∠CEB are right angles | 2. Given |

3. ΔAEB and ΔCEB are right Δs | 3. Definition of Right triangles |

4. $\displaystyle \overline{AB}$ ≅ $\displaystyle \overline{BC}$ | 4. Given |

5. $\displaystyle \overline{BE}$ ≅ $\displaystyle \overline{BE}$ | 5. Reflexive Property of Segment Congruence |

6. ΔABE ≅ ΔCBE | 6. Hypotenuse-Leg Congruence Theorem |

7. $\displaystyle \overline{AE}$ ≅ $\displaystyle \overline{CE}$ | 7. Corresponding parts of ≅ Δs are ≅ |

8. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{DE}$ [I'm kinda confused by this, but $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ has already been stated.] | 8. Definition of Perpendicular lines |

9. ΔAED and ΔCED are right Δs | 9. Definition of a Right Triangle |

10. $\displaystyle \overline{DE}$ ≅ $\displaystyle \overline{DE}$ | 10. Reflexive Property of Segment Congruence |

11. ΔAEB≅ ΔCEB | 11. Leg-Leg Congruence Theorem |

12. $\displaystyle \overline{AD}$ ≅ $\displaystyle \overline{CD}$ | 12. Corresponding parts of ≅ Δs are ≅ |

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

Re: Triangle Congruence Postulates -- Check please?

Quote:

Originally Posted by

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

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

http://i1137.photobucket.com/albums/...emexam4Q16.png **Statements** | Reasons |

1. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ | 1. Given |

2. ∠AEB and ∠CEB are right angles | 2. Given |

3. ΔAEB and ΔCEB are right Δs | 3. Definition of Right triangles |

4. $\displaystyle \overline{AB}$ ≅ $\displaystyle \overline{BC}$ | 4. Given |

5. $\displaystyle \overline{BE}$ ≅ $\displaystyle \overline{BE}$ | 5. Reflexive Property of Segment Congruence |

6. ΔABE ≅ ΔCBE | 6. Hypotenuse-Leg Congruence Theorem |

7. $\displaystyle \overline{AE}$ ≅ $\displaystyle \overline{CE}$ | 7. Corresponding parts of ≅ Δs are ≅ |

8. $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{DE}$ [I'm kinda confused by this, but $\displaystyle \overline{AC}$ ┴ $\displaystyle \overline{BD}$ has already been stated.] | 8. Definition of Perpendicular lines |

9. ΔAED and ΔCED are right Δs | 9. Definition of a Right Triangle |

10. $\displaystyle \overline{DE}$ ≅ $\displaystyle \overline{DE}$ | 10. Reflexive Property of Segment Congruence |

11. ΔAEB≅ ΔCEB | 11. Leg-Leg Congruence Theorem |

12. $\displaystyle \overline{AD}$ ≅ $\displaystyle \overline{CD}$ | 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