1. BY: JOE MARCIANO MAX HOLLANDER ANDREW FIEGLEMAN 3.2 Three Ways To Prove Triangles Congruent

2. The SSS postulate The first way to prove a triangle congruent is the SSS postulate. Also know as Side, Side, Side. The postulate says, 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 (SSS). What that means is if the corresponding sides of two triangles are congruent that makes the triangle congruent.

3. Is ∆DOG Yes they are by SSS. By the Reflexive property. Therefore both the triangles are congruent. ∆HOG ? O D G H

4. Sample Problem Given:, Prove: ∆HPI ∆LPI P H I L StatementsReasons 1.1. Given 2.2. Given 3.3. Reflexive 4. : ∆HPI ∆LPI4. SSS (1,2,3)

5. The SAS postulate The second way you can find a triangle congruent is the SAS postulate. Also known as Side, Angle, Side. The postulate says, 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 (SAS). What this means is that if two sides and the included angle are congruent in both triangles then the triangles are congruent.

6. Sample Problem Given: <OJE <MJE Prove: ∆JOE ∆JME J O E M StatementsReasons 1. <OJE <MJE1. Given 2.2. Given 3.3. Reflexive 4. ∆JOE ∆JME4. SAS

7. The ASA postulate The third way you can find a triangle congruent is the ASA postulate. Also known as Angle, Side, Angle. The postulate says, 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 (ASA). What that means is that if two angles and the included side are congruent in both triangles, the triangles are congruent.

8. Sample Problem Given: <BAC <DAC <ACB <ACD Prove: ∆ACB ∆ACD A B C D StatementsReasons 1. <BAC <DAC1.Given 2. <ACB <ACD2.Given 3.3.Reflexive 4. ∆ACB ∆ACD4.ASA(1,2,3)

9. Practice Problems 1. Given: C is the midpoint of Prove: ∆ACB ∆ACD 2. Given:<BAD is bisected by Prove: ∆ACB ∆ACD 3. Given:<BAD is bisected by is perpendicular to Prove: ∆BAC ∆DAC A B C D A B C D A B C D

10. Practice Problems Answers (1,2) 1. StatementsReasons 1. C is the midpoint of1. Given 2.2. Given 3.3. If a point is the midpoint of a segment, then it divides the segment into two congruent segments 4.4. Reflexive 5. ∆ACB ∆ACD5. SSS(2,3,4) 2.StatementsReasons 1. <BAD is bisected by1. Given 2.2. Given 3. <BAC <DAC 3.If a ray bisects an angle, then it divides the angle into two congruent angles. 4.4. Reflexive 5. ∆ACB ∆ACD5. SAS (2,3,4)

11. Practice Problem Answers (3) 3. StatementsReasons 1.<BAD is bisected by1. Given 2. Is perpendicular to2. Given 3.3. Reflexive 4.<BAC <DAC4. If a ray bisects an angle, then it divides the angle into two congruent angles 5. < ACB and <ACD are right angles 5.Perpendicular lines form right angles 6.<ACB <ACD 7. ∆ACB ∆ACD 6. If two angles are right angles, then they are congruent 7.ASA(3,4,6)

12. Work Cited Rhoad, Richard, George Milauskas, and Robert Whipple. Geometry for Enjoyment and Challenge. Evanston, Illinois: McDougal Littell, 1997. Print.