Two Right Triangles

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 51 of 60.

Right angles make AA easy. Two right triangles already have one pair of equal angles, because all right angles are equal. One more pair, often an angle the two triangles share, finishes the proof.

$Right triangle ABC with the right angle at C, and the height CD to AB with a right angle at D$

Here the squares sit at C and at D. Then ∠ADC = ∠ACB by All right angles are equal, ∠A is in both △ADC and △ACB (Reflexive property), and △ADC ∼ △ACB by AA. Mind the order: the right angle at D matches the right angle at C, so D and C take the same place in the two names.

Challenge

In △KMO the angle at M is a right angle. L lies on KM and N on KO, and ∠KLN is a right angle too. Prove that △KLN ∼ △KMO, then press Check.

Try it yourself

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

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

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA 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