Question

kimberlyskyy:
In triangles DEF and OPQ, ∠D ≅ ∠O, ∠F ≅ ∠Q, and segment DF ≅ segment OQ. Is this information sufficient to prove triangles DEF and OPQ congruent through SAS? Explain your answer.

Answer 1

@Hero

Answer 2

@Gustavo18 is there anything about the given scenario that you don't understand or have difficulty explaining? If so, please express your confusion.

Answer 3

I don't get how to use SAS to prove if triangles DEF and OPQ are congruent.

Answer 4

Quick question. Do you know the requirements to prove two triangles congruent using SAS? If so, what are the requirements?

Answer 5

Two sides and the included side of a triangle are congruent to two angles and the included angle for another triangle, then the triangle are congruent

Answer 6

From where did you reference this information?

Answer 7

My school notes

Answer 8

Did you leave your notes at school and recalling from memory?

Answer 9

No I have my notes

Answer 10

Okay screenshot the notes for SAS and post it here. I would like to see it.

Answer 11

Only screenshot the postulate from your notes. I'm curious

Answer 12

You can either screenshot or camera phone it

Answer 13

can I just type it because I'm being to put the photo in the file

Answer 14

You've already typed it. Now I would like to see it as printed from an official textbook. Upload the entire page that way I can verify that it was indeed published in an official school-approved textbook.

Answer 15

its not in a textbook it is in my notebook

Answer 16

And where did you get the information from?

Answer 17

From the school textbook

Answer 18

And where is your school textbook?

Answer 19

we don't get textbooks, they at school so every student in that Classe can use it

Answer 20

stay

Answer 21

Well, sorry to say but it appears that you copied those notes incorrectly.

Answer 22

really?

Answer 23

Compare what you wrote on paper to this;
\(\color{#0cbb34}{\text{Originally Posted by}}\) @Gustavo18
Two sides and the included side of a triangle are congruent to two angles and the included angle for another triangle, then the triangle are congruent
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 24

This is what I'm referring to when I say you copied your notes incorrectly. What you wrote on paper is not what you wrote here.

Answer 25

oh my bad

Answer 26

so is the notes In the paper correct?

Answer 27

If you copied verbatim from your school text, the notes should be correct.

Answer 28

oh ok

Answer 29

Suppose you have two triangles \(\triangle{ABC}\) and \(\triangle{DEF}\). To prove \(\triangle{ABC} \cong \triangle{DEF}\) You need to show the following:
1. At least two corresponding sides of both triangles congruent to each other
2. The angles between the two corresponding sides for both triangles congruent to each other.

Answer 30

For example if you are given that
\(BC \cong EF\) and \(AB \cong DE\) and \(\angle{A} \cong \angle{E}\)

Then you can conclude that the triangles are congruent by Side-Angle-Side Postulate.

Answer 31

But for the given scenario of the problem you're tasked with, are you given two sides of one triangle congruent to two sides of the other?

Answer 32

No

Answer 33

Exactly, so what can you conclude about your given problem?

Answer 34

That the proof is insufficient to prove triangles DEF and OPQ congruent through SAS

Answer 35

Because you are not given two sides of one triangle congruent to two sides of the other

Answer 36

But can it be proven using another postulate? If so, which?

Answer 37

ASA

Answer 38

Correct.

Answer 39

But would I have to include ASA on my answer to this question?

Answer 40

You should because then your instructor will know that you know how to recognize the difference between a SAS scenario and an ASA scenario.

Answer 41

Ok thank you for your help

Answer 42

You're welcome.