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# Warm-Up - PowerPoint PPT Presentation

Warm-Up. Day 13 - Triangle Congruence Postulates. SWBAT to prove triangles are congruent using SSS, SAS, ASA, AAS and HL. Mini-Assessment #3. Date: Thursday 10/31 (Periods 2, 4) or Friday 11/01 (Periods 1, 3) Covers: Day 10A – Pythagorean Theorem

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### Day 13 - Triangle Congruence Postulates

SWBAT to prove triangles are congruent using SSS, SAS, ASA, AAS and HL

Date: Thursday 10/31 (Periods 2, 4) or Friday 11/01 (Periods 1, 3)

Covers:

• Day 10A – Pythagorean Theorem

• Day 10B – Similar Right Triangles / Geometric Mean

• Day 11 – Parallel Lines & Transversals (Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, Same Side Interior Angles, etc)

• Day 12 – Isosceles Triangle, Exterior Angle, Triangle Sum

The of the measures of the exterior angles of a polygon, one at each vertex, is 360.

sum

Congruent triangles have 3 congruent sides and 3 congruent angles.

The parts of congruent triangles that “match” are called corresponding parts.

In a congruence statement

ORDER MATTERS!!!!

Everything matches up.

Corresponding Parts of Congruent Triangles are Congruent

B

If ABC  DEF,

then BC  ___

EF

A

C

D

F

E

B

If ABC  DEF,

then A  ___

D

A

C

D

F

E

B

If ABC  DEF,

then C  ___

F

A

C

D

F

E

If CAT  DOG,

then AC  ___

OD

BAT  MON

N

T  ___

_____  ONM

_____  MO

NM  ____

ATB

BA

TB

BCA   ____

____   GFE

EGF

CAB

MKL

_____   JKN

ABD

_____   CBD

All Three sides in one triangle are congruent to the three sides in the other triangle

Two sides and the INCLUDED angle of one triangle are congruent to two sides and the included angle of a second triangle.

A

A

S

S

A

A

Two angles and the INCLUDED side

(the side is in between the 2 marked angles)

A

A

A

S

S

Angle-Angle-Side (AAS) Congruence Postulate

Two Angles and One Side that is NOT included

There is one more way to prove triangles congruent, but it’s only for RIGHT TRIANGLES…Hypotenuse Leg

HL

SAS

ASA

AAS

HL

Your Only Ways To Prove Triangles Are Congruent

Reason: reflexive property

Vertical Angles

Reason: Vertical Angles are congruent

Practice Worksheet

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