Objectives
• Prove that two triangles are congruent
using the HL shortcut
• Use Corresponding Parts in Congruent
Triangles are Congruent (CPCTC) in
proofs
1
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.
2
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
3
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
4
Two-Column Proof with CPCTC Ex 1
QS ≅ QS
ΔPQS ≅ ΔRQS
CPCTC
5
Flowchart Proof with CPCTC Ex 1
6
Flowchart Proof with CPCTC Ex 2
Proof:
ΔPNQ ≅ ΔLMN
Given
CPCTC
QN ≅ MN
7
Two Column Proof with CPCTC Ex 2
Given
Reflexive Property
ΔUXW ≅ ΔUVW
HL
CPCTC
8