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Section 3.2 Three Ways to Prove Triangles Congruent

Section 3.2 Three Ways to Prove Triangles Congruent. By: Audra Nealon , Cierra Beck, Abby Pipcho *All figures not drawn to scale*. Included Angles and Sides. Included Angles. Included angles are formed when two lines meet at a vertex and form an angle.

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Section 3.2 Three Ways to Prove Triangles Congruent

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  1. Section 3.2Three Ways to Prove Triangles Congruent By: Audra Nealon, Cierra Beck, Abby Pipcho *All figures not drawn to scale*

  2. Included Angles and Sides Included Angles Included angles are formed when two lines meet at a vertex and form an angle. Ex. is the included angle of and A C B Included Sides Included sides are formed when two angles share a common side. Ex. is the included side of and

  3. The SSS Postulate If there exists a correspondence between the vertices of two triangles such that three sides of one triangle are congruent to the corresponding sides of the other triangle, the two triangles are congruent. A Z B C Y X

  4. A Example Proof Given: C is the midpoint of Prove D B C Statements Reasons 1. 2. C is the midpoint of 3. 4. 5. Given Given If a point is the midpoint of a seg, then it divides the seg. into two congruent segs. Reflexive SSS (1, 3, 4)

  5. The SAS Postulate If there exists a correspondence between the vertices of two triangles such that two sides and the included angle of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. Z A X Y B C

  6. Example Proof A B Given: Prove C D Statements Reasons Given Given Given Reflexive lines form right angles All right angles are congruent SAS (1, 4, 6) 1. 2. 3. 4. 5. and are right angles 6. 7.

  7. The ASA Postulate If there exists a correspondence between the vertices of two triangles such that two angles and the included side of one triangle are congruent to the corresponding parts of the other triangle, the two triangles are congruent. A Z B X C Y

  8. Example Proof A B Given: C is the midpoint of C Prove: E D Statements Reasons 1. 2. C is the midpoint of 3. 4. 5. Given Given If a point is the midpoint of a seg, then it divides the seg into two congruent segs. Vertical angles are congruent ASA (1,3,4)

  9. 1 Practice Proofs A E Given: D F Prove: C B A C Given: 2 B D F E Prove: Given: bisects 3 S R bisects T Prove: A

  10. Answer to Proof #1 A E D F C B Statements Reasons 1. Given 2. Given 3. Reflexive 4. SAS (1, 2, 3) 1. 2. 3. 4. Which Triangles are the coldest? ICE-sosceles triangles!

  11. A C Answer to Proof #2 B D F E Statements Reasons 1. Given 2. Addition 3. Given 4. Given 5. SSS (2, 3, 4) 1. 2. 3. 4. 5. What did the triangle say to the circle? Your life seems so pointless!!

  12. S Answer to Proof #3 R T A Statements Reasons 1. 2. 3. 4. 5. 6. bisects 1. Given 2. Given 3. If a ray bisects an angle, then it divides the angle into two congruent angles. 4. Same as 3 5. Reflexive 6. ASA (3, 4, 5) bisects Why are only three sides to a triangle?The fourth side wanted to be a square!

  13. Works Cited "Included Angle Definition - Math Open Reference." Table of Contents - Math Open Reference. Web. 15 Jan. 2011. “Included Side Definition - Math Open Reference.” Table of Contents - Math Open Reference. Web. 15 Jan. 2011. Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, IL: McDougal, Littell, 1991.

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