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# 2.6.2 SSS, SAS, ASA, AAS, and HL

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Congruent Triangles The student is able to (I can): Identify and prove congruent triangles given Three pairs of congruent sides (Side-Side-Side) Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side) Two angles and a side (Angle-Side-Angle and Angle- Angle-Side) A Hypotenuse and a Leg of a right triangle
Transcript
• Congruent Triangles

The student is able to (I can):

Identify and prove congruent triangles given

Three pairs of congruent sides (Side-Side-Side)

Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)

Two angles and a side (Angle-Side-Angle and Angle-Angle-Side)

A Hypotenuse and a Leg of a right triangle

• SSS Side-Side-Side

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

T

I

N

C

U

P

4

6

7 4

6

7

TIN CUP

• Example Given: , D is the midpoint of

Prove: FRD ERD

F

R

ED

FR ER FE

StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

1. 1. Given

2. D is midpt of 2. Given

3. 3. Def. of midpoint

4. 4. Refl. prop.

5. FRD ERD 5. SSS

FR ER

FE

FD ED

RD RD

• SAS Side-Angle-Side

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

L

H

S

U

T

A

LHS UTA

• Example Given: , A is the midpoint of

Prove: FAR EAM F

R

AM

E

FA EA RM

StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons

1. 1. Given

2. FAR EAM 2. Vertical s

3. A is midpt of 3. Given

4. 4. Def. of midpoint

5. FAR EAM 5. SAS

FA EA

RM

RA MA

• ASA Angle-Side-Angle

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

F

L

Y

B U

G

FLY BUG

• AAS angle-angle-side

If two angles and a nonnonnonnon----includedincludedincludedincluded side of one triangle are congruent to two angles and a non-included corresponding side of another triangle, then the triangles are congruent.

The non-included sides mustmustmustmust be corresponding in order for the triangles to be congruent.

N

IW

UO

Y

YOU WIN

• ASS angle-side-side

(we do not cuss in math class)

There is no ASS (or SSA) congruence theorem.

(unless the angle is a right angle see next slide)

• HL hypotenuse-leg

If the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

J

O

E

M

AC

JOE MAC

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