geom 5.5 sss and sas

5-5 SSS & SAS

Proving Triangles Congruent

Two geometric figures with exactly the same size and shape.

The Idea of a CongruenceThe Idea of a Congruence

A C

B

DE

F

How much do you 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 PartsCorresponding 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

Side-Side-Side (SSS) Similarity Theorem

If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

Side-Side-Side (SSS)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) Similarity Theorem

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

Side-Angle-Side (SAS)Side-Angle-Side (SAS)

1. AB DE

2. A D

3. AC DF

ABC DEF

B

A

C

E

D

F

included angle

Slide 1 of 2

The angle between two sides

Included AngleIncluded Angle

G I H

Name the included angle:

YE and ES

ES and YS

YS and YE

Included AngleIncluded Angle

SY

E

E

S

Y

Name That PostulateName That Postulate

SASSAS

SSSSSSSSASSA

(when possible)

Name That PostulateName That Postulate(when possible)

SASASS

SASSAS

SASASS

Reflexive Property

Vertical Angles

Vertical Angles

Reflexive Property SSSS

AA

Write a congruence statement for each pair of triangles represented.

A

B

FC

E

D

ΔACB ΔECD by SAS

B

A

C

E

D

Ex 6

Determine if whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it is not possible to prove that they are congruent, write not possible.

Slide 2 of 2

Slide 2 of 2

Slide 2 of 2

Slide 1 of 2

(over Lesson 5-5)

Slide 1 of 2

(over Lesson 5-5)