Objectives Prove that two triangles are congruent using the HL shortcut Use Corresponding Parts in Congruent Triangles are Congruent (CPCTC) in proofs

Hypotenuse-Leg Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

CPCTC CPCTC is an abbreviation of the phrase “Corresponding Parts of Congruent Triangles are Congruent.” ΔABC ≅ ΔDEF by AAS By CPCTC, all corresponding angles are congruent and all corresponding sides are congruent. ∠A ≅ ∠D ; BC ≅ EF ; AC ≅ DF

River Width Word Problem Some hikers come to a river in the woods. They want to cross the river but decide to find out how wide it is first. So they set up congruent right triangles. The figure shows the river and the triangles. Find the width of the river, GH. Since you’re given that the two right triangles are congruent, by CPCTC, JK = GH. So GH = 5 m

Two-Column Proof with CPCTC Ex 1 QS ≅ QS ΔPQS ≅ ΔRQS CPCTC

Flowchart Proof with CPCTC Ex 1

Flowchart Proof with CPCTC Ex 2 ΔPNQ ≅ ΔLMN Given CPCTC QN ≅ MN

Two Column Proof with CPCTC Ex 2 Given Reflexive Property ΔUXW ≅ ΔUVW HL CPCTC