Transcript Geometry Section 2.3 Notes

CHAPTER
2
2.3 Proofs Involving
Congruence
Copyright © 2014 Pearson Education, Inc.
Slide 4-1
Definition
Corresponding Parts of Congruent Triangles (and
thus Are Congruent).
We abbreviate this in a proof using cpoctac
(Corresponding Parts Of Congruent
Triangles Are Congruent).
Copyright © 2014 Pearson Education, Inc.
Slide 4-2
Example
Using Congruent Triangles
Given: AB bisects CAD
BA bisects CBD
Prove: 1  2
Copyright © 2014 Pearson Education, Inc.
Slide 4-3
Example
Using Congruent Triangles
Statements
Reasons
1. AB bisects CAD
1. Given
2. CAB  BAD
2. Definition of angle bisector
3. BA bisects CBD
3. Given
4. CBA  ABD
4. Definition of angle bisector
5. AB  AB
5. Reflexive Property
6. ACB  ADB
7. 1  2
6. ASA Postulate
7. cpoctac
Copyright © 2014 Pearson Education, Inc.
Slide 4-4
Proving Triangle Parts Congruent
Example
to Measure Distance
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?
Copyright © 2014 Pearson Education, Inc.
Slide 4-5
Proving Triangle Parts Congruent
Example
to Measure Distance
Given: TRS and TRL are right angles.
RTS  RTL
Prove: RS  RL
Copyright © 2014 Pearson Education, Inc.
Slide 4-6
Example
Proving Triangles Are Congruent
Statements
Reasons
1. RTS  RTL
1. Given
2. TR  TR
2. Reflexive Property of Congruence
3. TRS , TRL are rt. s 3. Given
4. TRS  TRL
4. All right angles are congruent.
5. TRS  TRL
5. ASA Postulate
6. RS  RL
6. cpoctac
Copyright © 2014 Pearson Education, Inc.
Slide 4-7