Can you prove that the two triangles are similar? Justify your answer.

Question

anonymous · Answer

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mathstudent55 · Answer

SAS Similarity is used here.
You need two parts: First you need the angle of o0ne triangle to be congruent to teh angle of the other triangle. You have that as marked on the pictures.

mathstudent55 · Answer

The second part is to show lengths of corresponding sides are in the same ratio.

mathstudent55 · Answer

The sides involved are the sides that form the congruent angles in both triangles.

mathstudent55 · Answer

You need to show that the ratio between two corresponding sides is the same as the ratio between the other two corresponding sides.

anonymous · Answer

But the side that has 20 doesn't have a side with a number to correspond

anonymous · Answer

But in the picture the sides with 4 and 5 are touching the congruent angle but the side with 20 isn't

hero · Answer

@adillie is correct. Those triangles are not similar. In the small triangle, the angle is between the given side lengths. In the other triangle, the corresponding angle is not between the given lengths.

anonymous · Answer

So my answer would be no I cant prove that they are similar...

hero · Answer

You could write it much better if you start with let ΔABC = small triangle. Let ΔDEF = large triangle. Then conclude with ΔABC ≁ ΔDEF

anonymous · Answer

@Hero Thank you. You are truly a lifesaver!

hero · Answer

That's not the whole proof, only the beginning and the end. You fill in the rest with your reasoning.

anonymous · Answer

I have a question that I closed but could really need your help on. Everyone started to confuse me more on the question. Can you help?

mathstudent55 · Answer

@adillie @hero When I saw this question last night, I glanced at the drawing too quickly and thought the congruent angles were the included angles in both triangles. addillie pointed out it wasn't the included angle in one triangle, which prompted me to look again at the drawing. adillie was absolutely correct. These triangles cannot be proven similar with the given information. When I was about to correct what I had written, OS went offline. To make matters worse, my computer froze and then shut down and restarted. Sorry about the mixup.