Two Right Triangles

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 54 of 63.

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.