4-4 & 4-5 Proving Triangles Congruent

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Presentation transcript:

4-4 & 4-5 Proving Triangles Congruent Objectives: 1. Use the SSS Postulate to test for triangle congruence. 2. Use the SAS Postulate to test for triangle congruence. 3. Use the ASA Postulate to test for congruence. 4. Use the AAS Theorem to test for congruence.

Side-Side-Side(SSS) Congruence – If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent. Included angle – the angle formed by two specific sides of a triangle. Side-Angle-Side (SAS) Congruence – 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

Included Side – the side between two specific angles. is the included side between and . Angle-Side-Angle(ASA) Congruence – 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. If and and included sides , then ΔABC ≅ΔDEF by the ASA Postulate.

These only work for Right Triangles. Leg-Leg (LL) Theorem - If the legs of one right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent. Leg-Angle (LA) Theorem - If one leg and an acute angle of one right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

Hypotenuse Leg (HL) Theorem - if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. Hypotenuse-Angle (HA) Theorem - If the hypotenuse and acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent.

Are the two triangles congruent Are the two triangles congruent? If so, name the postulate or Theorem that tells us. Yes No SSS Yes SSS

Yes SAS No

Yes SAS

Is ΔABC ≅ ΔKLM given the coordinates A(-3, 3), B(-1, 3), C(-3,1), K(1, 4), L(3, 4), M(1, 6)?

Angle-Angle-Side(AAS) Congruence – If two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of a second triangle, then the two triangles are congruent. If and and the non-included side , then ΔSTR ≅ΔUTR.

Identify the congruent triangles and name the postulate or Theorem used to prove congruence. Yes Yes AAS AAS Yes AAS Yes ASA

No

You now have five ways to show that two triangles are congruent. Definition of triangle congruence ASA Postulate SSS Postulate AAS Theorem SAS Postulate