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JM. BA. WC. OP. Warm up. No, corresponding sides are not congruent, and we can’t tell if the angles are congruent. No, the measures are not the same. Yes, angle measures are the same and the rays go to infinity.

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Warm up


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Presentation Transcript
warm up

JM

BA

WC

OP

Warm up

No, corresponding sides are not congruent, and we can’t tell if the angles are congruent.

No, the measures are not the same

Yes, angle measures are the same and the rays go to infinity

Yes, all corresponding sides are congruent and all corresponding angles are congruent.

Yes, all corresponding parts are congruent.

No, corresponding parts are not congruent.

L  A  J  F  M  X  P  B

 K  E  N  W  O  C

4 2 shortcuts in triangle congruency

4.2 Shortcuts in Triangle Congruency

Remember last time…

We learned that two polygons were congruent if EACH corresponding pair of angles were congruent AND each pair of corresponding sides were congruent.

Remember that you had to

LIST EACH PAIR?

Yikes! That could get very long and tedious (boring).

today
Today…

Today, you’re going to learn some shortcuts that apply to TRIANGLES ONLY.

These shortcuts, if used correctly, will help you prove triangle congruency.

Remember that congruency means EXACT size and shape… don’t confuse it with “similar”.

side side side

AC PX

AB PN

CB XN

Therefore, using SSS,

∆ABC= ∆PNX

X

A

3 inches

3 inches

5 inches

7 inches

~

P

C

B

7 inches

N

5 inches

~

~

~

~

=

=

=

=

Side Side Side

If 2 triangles have 3 corresponding pairs of sides that are congruent, then the triangles are congruent.

side angle side

X

CA XP

CB XN

C X

Therefore, by SAS,

∆ABC ∆PNX

60°

A

3 inches

5 inches

3 inches

P

N

60°

C

B

5 inches

~

~

~

~

=

=

=

=

Side Angle Side

If two sides and the INCLUDED ANGLE in one triangle are congruent to two sides and INCLUDED ANGLE in another triangle, then the triangles are congruent.

angle side angle

CA XP

A P

C X

Therefore, by ASA,

∆ABC ∆PNX

~

~

~

~

=

=

=

=

Angle Side Angle

If two angles and the INCLUDED SIDE of one triangle are congruent to two angles and the INCLUDED SIDE of another triangle, the two triangles are congruent.

X

60°

A

3 inches

3 inches

70°

70°

P

N

60°

C

B

remembering our shortcuts
Remembering our shortcuts

SSS

ASA

SAS

(just so you know, there are 2 abbreviations that are not used for congruence: AAA and SSA)

let s practice
Let’s practice

I need 3 volunteers to hand out white boards, markers and worksheets.

The worksheet is called ‘page 828’… we’ll do section 4.2 together.

your assignment
Your Assignment

Pg 220-222: 1-3, 8-19, 23-29