4.2 Triangle

Congruence by SSS and SAS

You will construct and

justify statements

about triangles using Side Side Side and Side

Angle SidePardekooper

First, we need to look at First, we need to look at some things.some things.

What makes two items congruent?

All the corresponding sides are congruent.

All the corresponding angles are congruent.

Pardekooper

Lets label the congruent Lets label the congruent partsparts

L

N M

P

Q R

N R

L P

M Q

NL RP

LM PQ

NM RQ

NLM RPQPardekooper

There is a theorem.There is a theorem.

If two angles of one triangle are congruent to two

angles of another triangle, then the third angle is

congruent

Pardekooper

If three sides of a triangle are If three sides of a triangle are congruent to three sides of congruent to three sides of another triangle, then the another triangle, then the triangles are congruent.triangles are congruent.

Lets look at some postulates

Side Side Side (SSS) Postulate

A

B

C

D

E

F

ABCABCDEFDEF

Pardekooper

If two sides and the included angle of a If two sides and the included angle of a triangle are congruent to two sides triangle are congruent to two sides and the included angle of another and the included angle of another

triangle, then the triangles are triangle, then the triangles are congruent.congruent.

Just one more postulate

Side Angle Side (SAS) Postulate

A

B

C

D

E

F

ABCABCDEFDEF

Pardekooper

Are the following congruent ?

Yes

SSSSAS

No

It’s the wrong angle

No

One angle is

off

Pardekooper

Now, its time for a proof.

Given: HFGiven: HFHJ, FGHJ, FGJI, H is midpoint of GI.JI, H is midpoint of GI.

Prove: Prove: FGHFGHJIHJIH

StatementStatement ReasonReason

1. Given1. HFHJ, FGJI

H is midpont of GI

2. Def. of midpoint2. GHHI

3. FGHJIH 3. SSS

HG

F J

I

Pardekooper

Given: EBGiven: EBCB, ABCB, ABDBDB

Prove: Prove: AEBAEBDCBDCB

Last proof.

StatementStatement ReasonReason

1. Given1. EBCB, ABDB

2. Vertical ’s2. EBACBD

3. AEBDCB 3. SAS

BE

A

D

C

Pardekooper