VIEWS: 7 PAGES: 13 POSTED ON: 9/12/2012
PROVING TRIANGLES CONGRUENT FOUR WAYS TO PROVE TRIANGLES ARE CONGRUENT Side-Side-Side Postulate (SSS) Side-Angle-Side Postulate (SAS) Angle-Side-Angle Postulate (ASA) Angle-Angle-Side Theorem (AAS) Side-Side-Side (SSS) If the sides of a triangle are congruent to the sides of a second triangle, then the two O triangles are congruent. Since the following information is true: A BO MA; OY AN ; BY MN Y B Then the two triangle must be congruent. BOY MAN M N Side-Angle-Side (SAS) If two sides and the included angle are congruent to two sides and the included angle of O another triangle, then the two triangles are congruent. A Y B WHAT IS AN INCLUDED ANGLE? M N Included Angles An included angle is the angle formed at the intersection of two sides of a triangle O So, the included angle between BO and BY would A be angle B. Y The included angle B between MA and MN would be angle M. M N Are these two triangles congruent? O A Y M N B If angle B is congruent to angle M, then the two triangles are congruent because of SAS. Angle-Side-Angle (ASA) If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent. O A WHAT IS AN INCLUDED SIDE? Y M N B Included Sides An included side between two angles is the side that is adjacent to both angles. O So, BY is the included side between angle B and angle Y Y B So are these two triangles congruent? O A Y M N B Yes, because two angles and the included side are congruent which makes the two triangles congruent by ASA. Angle-Angle-Side (AAS) If two angles and a nonincluded side of a triangle are congruent are congruent to two angles and a nonincluded side of another triangle, then the two triangles are congruent. O A Y B M N Are these two triangles congruent? O A Y B M N Since OY is not included between B and Y and AN is not included between M and N, these two triangles are congruent because of AAS. Angle-Side-Side THERE IS NO SUCH THING AS ANGLE SIDE SIDE BECAUSE YOU CAN’T USE THAT KIND OF LANGUAGE AT SCHOOL. Angle-Angle-Angle This cannot prove two triangles congruent. It just shows that they are similar. If both of these triangles are equiangular, they have three congruent angles. Are they congruent triangles?
Pages to are hidden for
"PROVING TRIANGLES CONGRUENT"Please download to view full document