Lesson 4-4: Using Corresponding Parts of Congruent Triangles Name ____________________________
Target: To use triangle congruence and corresponding parts of congruent triangles to prove that parts of two triangles
are congruent.
Is ABC  GHI ? How do you know?
Once you show two triangles are congruent, you can make conclusions about their other corresponding
parts because by definition, corresponding parts of congruent triangles are congruent.
(this is the ‘Reason’ in a proof for stating a 4th pair of parts is congruent)
You must FIRST prove the triangles are congruent!!
So let’s take a proof like we have seen before…
Given : AC  AD,
AB bisects CAD
a. ( FIRST show : ACB  ADB )
then PROVE : C  D
Statements
1. AC  AD
2. AB bisects CAD
3.
Reasons
1.
2.
3. Definition of Angle Bisector
4.
4. Reflexive Property
5.
5.
6.
6.
The following is called a FLOW
CHART PROOF;
Thales, a Greek philosopher, is said to have developed a method to measure the distance to a ship at sea. He
made a compass by nailing two sticks together. Standing on top of a tower, he would hold one stick vertical
and tilt the other until he could see the ship S along the line of the tilted stick. With this compass setting, he
would find a landmark L on the shore along the line of the tilted stick. How far would the ship be from the base
of the tower?
Given: TRS and TRL are right angles, RTS  RTL
Prove: RS  RL
Statements
Reasons
1. RTS  RTL
1.
2. TR  TR
2.
3. TRS and TRL are right angles
3.
4. TRS  TRL
4.
5. TRS  TRL
5.
6. RS  RL
6.
a) Write a congruence statement to state what 2 triangles are congruent to each other. Then b) state a 4th pair of
sides or angles that are congruent by C
1)
2)
EAT  _____
by ______________ postulate
so ______  ______ because
JUN  _____
by ______________ postulate
so ______  ______ because
corresponding parts of congruent triangles are congruent
____________________________________
Given: AB  AC , M is the midpoint of BC
Prove: AMB  AMC
Statements
Reasons
1) AB  AC , M is the midpoint of BC
1)
2) ______________________
2) Definition of midpoint
3) ______________________
3) Reflexive
4)
BMA  ______
5) ___________________________________
4)__________________
5) ________________________________________
D
A
Given : AB  DB, CB  EB
Prove : A  D
B
E
C
Statements
Reasons
L
Given : LF  LH , F  H , LSH and LSF are right angles
Prove : LS bisects FLH
F
Statements
Reasons
S
H
Hmwk: pgs.246-248 # 5-7, 11, 12, 14, 25, 27-32