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How do I find which postulate or theorem goes with each triangle?

How do I find which postulate or theorem goes with each triangle?-example-1
User ZiggZagg
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1 Answer

10 votes
10 votes

First, let's go over the postulates/theorems:

SSS - If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

SAS - If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

AAS - If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

ASA - If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

HL - Two right triangles that have a congruent hypotenuse and a corresponding congruent leg are congruent.

Now, looking at the figures:

a.

As indicated with the single, double, and triple lines on the sides, the triangles are congruent by side-side-side postulates. So,

SSS

b.

These are right triangles.

They have congruent hypotenuse and another side (leg) that is congruent.

So, it goes by the postulate HL. So,

HL

c.

This one doesn't fall into any of the theorem/postulate. We can say "cannot be determined".

User Hercules
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