Geometry4.5 Other Methods of Proving

Triangles Congruent

In Chapter 3 you were introduced to this corollary:if 2 angles of one triangle are congruent to 2 angles of

another triangle, then the 3rd angles are congruent.

We have 2 congruent angles and one congruent side………but the side is not the included side. Can anything be proved?

This would allow us to conclude that angles A and B are congruent, and would create an ASA congruence.

AB

So the moral to the story is: any two congruent angles and one congruent side gives you congruent triangles.

The AAS (Angle-Angle-Side) Theorem

X

YZ

A

CB

ABC

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

XYZ

LEG

LEG

HYPOTENUSE

Right Triangle Vocabulary

Remember the definition of a right triangle It has one right angle

The HL (Hypotenuse - Leg) Theorem

ABC

If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangles are congruent.

XYZ

A

B C

X

Y Z

Summary of Ways to Prove Triangles Congruent

All triangles Right triangles

SSS PostSAS PostASA PostAAS Thm

HL Thm

1 42 3

Given: <2 <3

<4<1

1 32 4

same side

Name the congruence

∆ LMN congruent to ∆ PNM by ASA

L

M

Q

P

N

OVERLAPPING TRIANGLES

||BC AD

DC AB C

D

A

B

1. Given:

Prove:

DB

KBAJAB

3. Given:

Prove:

J K

BA

21 KJ

1 2

4. Given: Angles M and R are right angles

Prove:

SR TM

SMR TRM

TS

RM

Homework

pg. 142 CE #1-13

WE # 1-8

Bring CompassJust a reminder of what’s allowed in the bins:  EMPTY plastic bottles, aluminum cans, and paper. Whats NOT allowed:  wrappers, gum, Ziploc baggies, half-empty beverages.  If these items are in the bins, then the whole bin gets dumped into the trash. Last week, I spent the first 5 minutes of each class demonstrating what goes in each receptacle.  Since this small demonstration, my students have been very good about proper placement of waste items in my classroom.

Let’s do a few from the homework

Turn to pg. 142 CE #5, #6 , #10

Now pg. 143 WE #2