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.

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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.

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LHS UTA

Example Given: , A is the midpoint of

Prove: FAR EAM F

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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.

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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.

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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.

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JOE MAC