# Unit 2 Part 4 Proving Triangles Congruent. Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles.

Unit 2 – Triangle Congruence – SAS
Unit 2 – Triangle Congruence – SAS

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Unit 2 Part 4 Proving Triangles Congruent

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Angle – Side – Angle Postulate If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then they are congruent by ASA. Included means between

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Example of ASA A F E D C B The side is between the angles.

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Angle – Angle – Side Postulate If two consecutive angles and a side of a triangle are congruent to two consecutive angles and a side of another triangle, then the triangles are congruent by AAS. Consecutive means one after another. Note: the side is NOT between the angles

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Example of AAS F E D C B A The side is not between the angles.

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Recall Reflexive Property : such as segment AB is congruent segment AB Vertical Angles are congruent such as angle G is congruent to angle H B A D C GH

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A S A

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A A S

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Hypotenuse-Leg Theorem (HL Theorem) If the hypotenuse and leg of a right triangle is congruent to the hypotenuse and leg of another right triangle then they are congruent.

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R H L

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CPCTC Corresponding Parts of Congruent Triangles are Congruent. Once you prove two triangles congruent, then all of their corresponding parts are congruent.

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SSS Side – Side – Side SAS Side – Angle – Side AAS Angle – Angle – Side ASA Angle – Side – Angle HLT Hypotenuse – Leg – Theorem Reflexive Property Vertical Angles CPCTC (corresponding parts of congruent triangles are congruent) What you should remember

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S S A

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Statement Reason

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