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Published byTitus Godbolt Modified over 2 years ago

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Proving Triangles Congruent SSS Postulate, SAS Postulate ASA Postulate, AAS Theorem & HL Theorem

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Side - Side - Side Postulate If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. ABC DEF A C B F E D

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SSS Example: E T I K ITK ETK

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Side - Angle - Side Postulate If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are JKL MNO O N M J L K

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SAS Example ARK ? ERN K N E R A

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Angle - Side - Angle Postulate If two angles and the included side of one triangle are to two angles and the included side of another triangle, then the triangles are PQR STU U T S RQ P

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ASA Example M Y R A AY Bisects < MAR YMA ? YRA

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Angle - Angle - Side Theorem If two angles and a nonincluded side of one triangle are to two angles and the corresponding nonincluded side, then the triangles are XYZ JAC C J A Z Y X

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AAS Example K Y R E RKY ? KRE

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Hypotenuse-Leg Theorem If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are RPW SBM R P W S B M

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QMC ? QHC Q H C M HL Example

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Example 1 M E K I IEM ? IEK Property? SAS

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Example 2 RBA ? IBT Property? ASA R T I B A

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Example 3 MOU ? None Property? None: SSA isn’t a property M E S U O

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Example 4 RIK ? SKI Property? SSS K S I R

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Example 5 SIL ? LAS Property? AAS L A S I

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RBI ? GBI Property? HL I R G B Example 6

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MISSING PARTS What information do you need to prove the following triangles are congruent by SAS? Q W E RT

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MISSING PARTS What information do you need to prove the following triangles are congruent by ASA? A S D F G 63 o

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MISSING PARTS What information do you need to prove the following triangles are congruent by AAS? T Y U I

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MISSING PARTS What information do you need to prove the following triangles are congruent by SSS? Y C V B 6 6

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MISSING PARTS What information do you need to prove the following triangles are congruent by HL? Q H C M

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