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ASA or AAS?

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 25 of 63.

When the givens are written in words instead of drawn, the figure carries no marks, and you have to place each fact yourself. Find the two angles' vertices, then find the side.

$Triangles ABC and DEF with no marks$

Say you are given ∠B = ∠E, ∠C = ∠F and AB = DE. The angles are at B and C, so the included side would be BC. AB is a different side, so this is AAS. Had the given been BC = EF, it would be ASA. Both rules prove congruence; the board only asks you to name the right one.

Challenge

The figure has no marks. You are given ∠QRP = ∠TUS, ∠RPQ = ∠UST and PQ = ST. The statements are written; give each its reason, then press Check.

Try it yourself

$Write the proof$

Write the proof

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape Matching Sides Matching Angles What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS RuleASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs

AA Similarity Two Right Triangles SSS Similarity SAS Similarity Similar, Then Find Recap: Similarity