Download Holt McDougal Geometry 4-7

4-7 Triangle Congruence: CPCTC
Materials:NEW WARM UP SHEET, Pencil/Pen,
NOTES SHEET WITH THEOREMS
GEL 12/5
G: I CAN USE CPCTC TO PROVE
PARTS OF TRIANGLES ARE
CONGRUENT.
E: REAL-WORLD PROBLEMS
Warm Up 12/5
1. If ∆ABC  ∆DEF, then A  ? and
BC  ? .
2. List methods used to prove two
triangles congruent
L: PROBLEM SOLVING
HOMEWORK: FINISH PROBLEM SOLVING IF
NOT DONE IN CLASS… DUE TOMORROW
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
CPCTC is an abbreviation for the phrase
“Corresponding Parts of Congruent
Triangles are Congruent.” It can be used
as a justification in a proof after you have
proven two triangles congruent.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Remember!
SSS, SAS, ASA, AAS, and HL use
corresponding parts to prove triangles
congruent. CPCTC uses congruent
triangles to prove corresponding parts
congruent.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Example 1: Engineering Application
A and B are on the edges
of a ravine. What is AB?
One angle pair is congruent,
because they are vertical
angles. Two pairs of sides
are congruent, because their
lengths are equal.
Therefore the two triangles are congruent by
SAS. By CPCTC, the third side pair is congruent,
so AB = 18 mi.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Check It Out! Example 1
A landscape architect sets
up the triangles shown in
the figure to find the
distance JK across a pond.
What is JK?
One angle pair is congruent,
because they are vertical
angles.
Two pairs of sides are congruent, because their
lengths are equal. Therefore the two triangles are
congruent by SAS. By CPCTC, the third side pair is
congruent, so JK = 41 ft.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Example 4: Using CPCTC In the Coordinate Plane
Given: D(–5, –5), E(–3, –1), F(–2, –3),
G(–2, 1), H(0, 5), and I(1, 3)
Prove: DEF  GHI
Step 1 Plot the
points on a
coordinate plane.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Step 2 Use the Distance Formula to find the lengths
of the sides of each triangle.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
So DE  GH, EF  HI, and DF  GI.
Therefore ∆DEF  ∆GHI by SSS, and DEF  GHI
by CPCTC.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Check It Out! Example 4
Given: J(–1, –2), K(2, –1), L(–2, 0), R(2, 3),
S(5, 2), T(1, 1)
Prove: JKL  RST
Step 1 Plot the
points on a
coordinate plane.
Holt McDougal Geometry
4-7 Triangle Congruence: CPCTC
Check It Out! Example 4
Step 2 Use the Distance Formula to find the lengths
of the sides of each triangle.
RT = JL = √5, RS = JK = √10, and ST = KL
= √17.
So ∆JKL  ∆RST by SSS. JKL  RST by
CPCTC.
Holt McDougal Geometry