Triangle Congruence - ASA and AAS. We've just studied two postulates that will help us prove congruence between triangles. However, these postulates were. Explore properties of triangle congruence. Understand and practice flow proofs. Understand and practice two-column proofs. Information for congruent triangle proofs Learn with flashcards, games, and more — for free.

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## Congruent Triangle Proofs (Part 1)

Sometimes we will just need to show that two triangles are congruent. Other times, we will need to use the congruence to then show that some other fact about the triangles is also true. This is not enough information to decide if two triangles are congruent!

The SAS Postulate required congruence of two sides and the included angle, congruent triangle proofs the ASA Postulate requires two angles and congruent triangle proofs included side to be congruent.

An illustration of this postulate is shown below.

Let's practice using the ASA Postulate to prove congruence between two triangles. Let's start off this problem by examining congruent triangle proofs information we have been given. Since segments PQ and RS are parallel, this tells us that we may need to use some of the angle postulates we've studied in the past.

Now, let's look at the other piece of information we've been given. PRQ is congruent to? Let's further develop our plan of attack. We have been given just one pair of congruent angles, so let's congruent triangle proofs for another pair that we can prove to be congruent.

## | CK Foundation

PQR is congruent to? SAS Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then congruent triangle proofs triangles are congruent.

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

Definition of angle bisector 3. Segment OK is congruent to segment OK 3. The following diagrams show the Rules for Triangle Congruency: Congruent triangle proofs down the page for more examples, solutions, and proofs.

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The SSS rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.