If triangles ABC, RST congruent to XYZ, then congruent to...

[Thalleen]

Hi there! I am in my College II Math class and I am really struggling with geometry. One question I am not understanding how to solve is as follows:

"Prove that, if two triangles ABC and RST are congruent to the same triangle XYZ, then they are congruent to each other."

What do they mean by that and how would I "prove" it? There weren't any triangles for this question and I am unsure on how to answer it. I haven't had a geometry class since the late 80s so I am really stuck on this. I did have a college algebra course a few years ago, but I forgot alot of it. Anyway, if anyone could clarify this for me, I would really appreciate it! I don't need to turn it in until Saturday so I have a few days. Thank you! Lisa

p.s. We are reading out of the book "Elementary Geometry for College Students, 4th Edition, Alexander/Koeberlein

 

[tkhunny]

Re: Geometry Question

You must study the axioms and theorems.

Is "congruence" transitive? That IS what you are trying to prove.

You will need a healthy sampling of "CPCTAC". Have you seen that?

 

[Thalleen]

Re: Geometry Question

Thank you for your response. I wish math came easily for me considering we use it all the time as an interior design student but it is not coming that easily since I am learning new stuff. I read some more last night and I read about the CPCTC...is that what you mean or have i just not gotten to what you are talking about yet? : ) Believe me, I am usually not this naive but, as I mentioned, I haven't had a math class (besides college algebra 3 years ago) in over 23 years. I am stumped on this one. I appreciate the help and the tips. Thank you! I will let you know if I do it right or not. : ) Lisa

 

[Denis]

Re: Geometry Question

TK, are you saying there is a theorem that says the likes of:
"if A = X and B = X, then A = B"?

 

[tkhunny]

Re: Geometry Question

No, that also requires "=" to be commutative.

If A = X and X = B, then A = B.

 

[masters]

Re: Geometry Question

Hi there! I am in my College II Math class and I am really struggling with geometry. One question I am not understanding how to solve is as follows:

"Prove that, if two triangles ABC and RST are congruent to the same triangle XYZ, then they are congruent to each other."

Thank you! Lisa

Hello Lisa,

Here's the proof:

Prove:

\(\displaystyle If \ \ \bigtriangleup ABC \cong \bigtriangleup XYZ \ \ and \ \ \bigtriangleup RST \cong \bigtriangleup XYZ, \ \ then \ \ \bigtriangleup ABC \cong \bigtriangleup RST\)

Statement 1:

\(\displaystyle \bigtriangleup ABC \cong \bigtriangleup XYZ \ \ and \ \ \bigtriangleup RST \cong \bigtriangleup XYZ\)

Reason 1: Given

Statement 2:

\(\displaystyle \overline{AB}\cong\overline{XY} \ \ and \ \ \overline{RS}\cong\overline{XY}\)

\(\displaystyle \overline{BC}\cong\overline{YZ} \ \ and \ \ \overline{ST}\cong\overline{YZ}\)

\(\displaystyle \overline{AC}\cong\overline{XZ} \ \ and \ \ \overline{RT}\cong\overline{XZ}\)

Reason 2: Corresponding Parts of Congruent Triangles are Congruetn (CPCTC)

Statement 3:

\(\displaystyle \overline{AB}\cong\overline{RS}\)

\(\displaystyle \overline{BC}\cong\overline{ST}\)

\(\displaystyle \overline{AC}\cong\overline{RT}\)

Reason 3: Substitutions from Statement 2

Statement 4:

\(\displaystyle \therefore \ \ \bigtriangleup ABC \cong \bigtriangleup RST\)

Reason 4: If 3 sides of one triangle are congruent to 3 sides of another triangle, then the two triangles are congruent. (SSS Postulate)