1

Objective – To prove triangles congruent using SSS and SAS.

SSS Congruence PostulateIf 3 sides of a triangle are congruent to 3 sidesof another triangle, then the triangles are congruent.

SSS

If 3 sides are

3 angles will be

triangles will be

If 3 angles are

sides are notnecessarily

noconclusion

AAA

Reasons

Given: AD DCB is midpoint of AC Prove: ABD CBD

Statement

1) B is midpoint AC Given

A B

D

C

2) AB BC

3) BD BD

4) AD DC Given

Def. of Midpoint

Reflexive Prop. of

SSS Postulate5) ABD CBD

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X

1) Construct

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X

1) Construct

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X

1) Construct

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SASB

Steps

A

X

C

1) Construct

Lesson 4-4

Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014

2

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X

1) Construct 2) Copy adjacent side length

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X Z

1) Construct 2) Copy adjacent side length

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X Z

3) Copy other adjacent side

1) Construct 2) Copy adjacent side length

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

Steps

AC

X Z

3) Copy other adjacent side

1) Construct 2) Copy adjacent side length

B

SAS Congruence PostulateIf 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

Construction – Copy a Triangle Using SAS

StepsABC XYZ by SAS

AC

X Z

Y

3) Copy other adjacent side

1) Construct 2) Copy adjacent side length

Given: PM LN, LP PN, L NProve: LMP NMP

Statement

1) PM LN Given2) PML & PMN are rt. s 3) PML PMN All rt s are

L M

P

N

Reasons

Def. of lines3) PML PMN 4) L N

7) PM PM

5) LPM NPM

Given

6) LP PN

All rt. s are

Given

Reflexive Prop of 8) LMP NMP

Third Angles Thm.

SAS Postulate

Lesson 4-4

Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014

3

How can the triangles be proved congruent?

1)

SSS

3)

SAS

2)

SAS

4)

No Conclusion

How can the triangles be proved congruent?

5)

SAS

7)

SAS

6)

No Conclusion

8)

No Conclusion

Show that HIJ LMN if x 5.

H J

I N

3x 4

10 14

2x

L

M

19

4x 6

ML 2x 2(5) 10 HI ML HI ( )

MN 4x 6 4(5) 6 14 IJ MN IJ

HJ 3x 4 3(5) 4 19 LN HJ LN

HIJ LMN by SSS

Show that ABC JKL if n 4.

B C

A K

3n

58 142n 2

L

J

126n 8

2JL 2 2(4) 2 14 AC AC JL

32

2JL n 2 2(4) 2 14 AC AC JL

BC 3n 3(4) 12 KL BC KL

L 6n 8 6(4) 8 32 C C L

ABC JKL by SAS

Lesson 4-4

Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014