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Proving Triangles Congruent

Learn about triangle congruence criteria such as SSS, AAS, HL, SAS, and ASA for proving triangles are congruent. Master the techniques with examples.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent

  2. Included Angles & Sides Included Angle: * * * Included Side:

  3. SIDE SIDE SIDE(SSS) A D F B C E If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent.

  4. ANGLE ANGLE SIDE(AAS) A D B C F E If the if two consecutive angles and a side not between them on one triangle are congruent to two consecutive angles and a side not between them on a second triangle, then the triangles are congruent. 4

  5. HYPOTENEUSE LEG(HL) D A B C F E If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. 5

  6. SIDE ANGLE SIDE(SAS) A D B C F E If two sides and the included angle of one triangle are congruent to the two sides and the included angle of another triangle, then the triangles are congruent. 6

  7. ANGLE SIDE ANGLE(ASA) A D B C F E If two angles and the included side of one triangle are congruent to the two angles and the included side of another triangle, then the triangles are congruent. 7

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