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
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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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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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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