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NAME:____________________________________! DATE: 2/15 ASSIGNMENT: Types of Congruent Triangles: SSS, SAS, HL DIRECTIONS: Sometimes we are not told if triangles are congruent, so we must know what exactly makes a triangle congruent. Here are two ways to find out: Side-Side-Side (or SSS): If all the sides of a triangle are congruent, then the two triangles are congruent. This one’s the easiest to understand. Side-Angle-Side (or SAS): If two sides and their INCLUDED angle are congruent, then the two triangles are congruent. An INCLUDED angle is the angle in between the two congruent sides. For example: Here the pairs of congruent sides are Side RS = Side SU and Side QS = Side ST. Angle S = Angle S because they are vertical angles, AND Angle S is the INCLUDED angle because it is in between the two sides. Hypotenuse-Leg (or HL): If a hypotenuse and leg in a RIGHT triangle are congruent to the hypotenuse and leg of another RIGHT triangle, then those two RIGHT triangles are congruent. 1.) Is Angle N an “included” angle? Why or Why not? ___________________________________ __________________________________________________ 2.) Are Triangle JKM and Triangle LKM congruent? Why or Why not? __________________________________ __________________________________________________ If you answered yes, are they congruent because of SSS or SAS or AAS or ASA or HL (circle one) 3.) Are these two triangles congruent? Why or Why not? _____________________________________ _____________________________________________________ If you answered yes, are they congruent because of SSS or SAS or AAS or ASA or HL (circle one) 4.) Draw an example of two triangles that are congruent by HL below. NAME:____________________________________! DATE: 2/15 ASSIGNMENT: Types of Congruent Triangles: ASA and AAS DIRECTIONS: Sometimes we are not told if triangles are congruent, so we must know what exactly makes a triangle congruent. Here are two ways to find out: Angle-Side-Angle (or ASA): If two triangles have two angles and their INCLUDED side congruent, then the two triangles are congruent. An INCLUDED side is the side in between the two congruent angles. Angle-Angle-Side (or AAS): If two triangles have two angles and their NON-INCLUDED side congruent, then the two triangles are congruent. A NON-INCLUDED side is a side adjacent to two congruent angles. 5.) Is Side AB an “included” side? ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! Why or Why not? ___________________________________ ! ! ! ! ! ! ! ! ! __________________________________________________ B ! ! ! ! ! ! ! ! ! ! ! ! 6.) Are these two triangles congruent? Why or Why not? __________________________________ __________________________________________________ If you answered yes, are they congruent because of SSS or SAS or AAS or ASA or HL (circle one) 7.) Are these two triangles congruent? Why or Why not? _____________________________________ _____________________________________________________ If you answered yes, are they congruent because of SSS or SAS or AAS or ASA or HL (circle one) 8.) Are these two triangles congruent? Why or Why not? _____________________________________ _____________________________________________________ If you answered yes, are they congruent because of SSS or SAS or AAS or ASA or HL (circle one) A ! ! C NAME:____________________________________! Answers: 1.) Yes. 2.) Yes. 3.) Yes. 4.) Many examples. Come tutorials if you need help. 5.) Yes. 6.) Yes. 7.) Yes. 8.) Yes. DATE: 2/15