Ch 5. Proving Triangles Congruent (Sec 5.4 – Sec 5.6)

Objectives: What we’ll learn… Identify corresponding parts of congruent triangles. Use SSS and SAS tests for congruence. Use ASA and AAS tests for congruence.

Two geometric figures with exactly the same shape and size. The Idea of a Congruence A C B DE F NOT Congruent!!! B A C E D F Yes, they are Congruent.

Why Congruence? When factory manufactures cars, each car must be identical (congruent)…… If not congruent = defects= Company losing $$$$$$

Why triangles? It’s a simple polygon!!!

How much do you need to know... need to know about two triangles to prove that they are congruent?

You learned that if all six pairs of corresponding parts (sides and angles) are congruent, then the triangles are congruent. Corresponding Parts  ABC   DEF B A C E D F 1.AB  DE 2.BC  EF 3.AC  DF 4.  A   D 5.  B   E 6.  C   F

Do you need all six ? NO ! SSS SAS ASA AAS

Side-Side-Side (SSS) 1. AB  DE 2. BC  EF 3. AC  DF  ABC   DEF B A C E D F

Side-Angle-Side (SAS) 1. AB  DE 2.  A   D 3. AC  DF  ABC   DEF B A C E D F included angle

The angle between two sides Included Angle  G G  I I  H H

Name the included angle: YE and ES ES and YS YS and YE Included Angle SY E  E E  S S  Y Y

Angle-Side- Angle (ASA) 1.  A   D 2. AB  DE 3.  B   E  ABC   DEF B A C E D F included side

The side between two angles Included Side GI HI GH

Name the included side:  Y and  E  E and  S  S and  Y Included Side SY E YE ES SY

Angle-Angle-Side (AAS) 1.  A   D 2.  B   E 3. BC  EF  ABC   DEF B A C E D F Non-included side

Warning: No SSA Postulate TRIANGLES NOT CONGRUENT There is no such thing as an SSA postulate!

Warning: No AAA Postulate A C B D E F There is no such thing as an AAA postulate! All congruent angles, but NOT congruent in size.

The Congruence Postulates  SSS correspondence  ASA correspondence  SAS correspondence  AAS correspondence  SSA correspondence  AAA correspondence

Name That Postulate SAS ASA SSS SSA (when possible)

Name That Postulate (when possible) ASA SAS AAA SSA

Name That Postulate (when possible) SAS SAS SAS Reflexive Property Vertical Angles Reflexive Property SSA

HW: Name That Postulate (when possible)

HW: Name That Postulate

Included Angle

Included Side

Hexagon vs. Pentagon

Hint: No AAA Postulate

Let’s Practice Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS:  B   D For AAS: A  F A  F AC  FE

HW Indicate the additional information needed to enable us to apply the specified congruence postulate. For ASA: For SAS: For AAS:

This powerpoint was kindly donated to is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.