SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 1

Daily Warm-Up

1. What two conditions must be met to show congruent polygons?

___________________________. ___________________________. 2. If MEAT SHOP what can you

determine? 3. Name and illustrate one congruence

shortcut for triangles.

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 2

Showing Triangles Congruent

At the end of this lesson, you should be able to prove two triangles are congruent by using SAS or SSA (ASS). Which one works?

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 3

The six different combinations of congruent pairs of three parts are diagrammed below.

Side-Side-Side * Angle-Angle-Angle * Side-Angle-Side

SSS AAA CBD

Side-Side-Angle Angle-Side-Angle Angle-Angle-Side

CBD

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 4

SSide-AAngle-Side Postulate If two sides and the included angle of one

triangle correspond and are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. (SAS Postulate)

Side-Angle-Side

ALERT A note on what it means to be an included angle:

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 5

The included angle means the angle between two sides. In other words, the angle is actually formed by the two sides.

What about SSA/ASS (Side Side Angle/Angle Side Side)?

.

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 6

If two triangles have two congruent sides and a congruent non-included

angle, then triangles are NOT NECESSARILY congruent

In which pair of triangles pictured below could you use the Side Angle Side postulate (SAS) to prove the

triangles are congruent?

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 7

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 8

Showing Two ∆s Congruent

Given: WO ≡ NEM is the midpoint of

WN and OEAre the two triangles congruent? Explain.Write a congruence

statement.

W O

M

E N

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 9

Showing Triangles Congruent

T E

A M

Given: TE //AM

∆ MAT ________

Reason: _________

1

2

SSS & SAS Congruence Postulates

Mrs. McConaughy Geometry 10

Wrap Up: Final Checks for Understanding

1. What two conditions must be met to determine congruent polygons?

2. Name and illustrate two congruence shortcuts for showing two triangles are congruent.

3. Which two combinations of sides and angles cannot be used to determine congruent triangles