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Proving Triangles Congruent

Proving Triangles Congruent. 9.3.3.6 Know and apply properties of congruent and similar figures to solve problems and logically justify results. . Guiding Question: How can we prove 2 triangles are congruent to each other?.

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Proving Triangles Congruent

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  1. Proving Triangles Congruent 9.3.3.6 Know and apply properties of congruent and similar figures to solve problems and logically justify results.

  2. Guiding Question: How can we prove 2 triangles are congruent to each other? • Lesson Obj.: IWBAT prove triangles are congruent using SSS, SAS, ASA, AAS, or HL theorem.

  3. Guiding Question: How can we prove 2 triangles are congruent to each other? Side-Side-Side Postulate (SSS) Attempt to prove that segments are congruents. SSS Postulate - If 3 sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent.

  4. Guiding Question: How can we prove 2 triangles are congruent to each other? Side-Angle-Side Postulate Prove 2 sides and the angle in-between! (SAS) Postulate – if 2 sides and the included angle of a triangle are congruent to 2 sides and the included angle of another triangle, the triangles are congruent.

  5. Guiding Question: How can we prove 2 triangles are congruent to each other? Prove 2 angles are congruent and the side in-between Angle-Side-Angle Postulate • (ASA) Postulate – If 2 angles and the included side of a triangle are congruent to 2 sides and the included side of another triangle then the triangles are congruent.

  6. Guiding Question: How can we prove 2 triangles are congruent to each other? Angle-Angle-Side Postulate Prove 2 angles and the adjacent side! AAS Post. – If 2 angles and a non-included side of a triangle are congruent to 2 angles and a non-included side of another triangle then the triangles are congruent.

  7. Guiding Question: How can we prove 2 triangles are congruent to each other? Hypotenuse Leg Theorem ONLY IN RIGHT TRIANGLES! • (HL) Thm – If the hypotenuse and a leg of a RIGHT triangle are congruent to the hypotenuse and a leg of another RIGHT triangle, then the triangles are congruent.

  8. Guiding Question: How can we prove 2 triangles are congruent to each other? • Theorems that do not exist • AAA Theorem (Different Size triangles) • SSA Theorem (Hinge Theorem) • Theorems to be used • SSS • SAS • ASA • AAS • HL

  9. Guiding Question: How can we prove 2 triangles are congruent to each other? Why are these 2 triangles congruent? Why are these 2 triangles congruent?

  10. Guiding Question: How can we prove 2 triangles are congruent to each other? Why are these 2 triangles congruent? Why aren’t these 2 triangles congruent? What info am I given?

  11. Guiding Question: How can we prove 2 triangles are congruent to each other? • Look at the in-class packet on proofs. • Assignment: Triangle Congruence WS • Triangle Congruence WS (2) • Proof Packet

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