Triangle Congruence Guided Notes

Name: Date: 4.2 & 4.5 Ways to Prove Triangles Congruent  I can use SSS, SAS, ASA Postulates or AAS, HL theorems to prove 2 triangles are congruent We can use CPCTC to show that the matching parts of the congruent triangles are congruent as well, but how do we show that the triangles are congruent in the first place? Until now, we could prove triangles are congruent by showing all the ______________ are congruent and all the ______________ are congruent. Side-Side-Side Congruence Postulate (SSS) If three _______________ of one triangle are ___________________ to three ________________ of another triangle, then the two triangles are _____________________. If Side ______________, and Side ______________, and Side ______________, then ___________________. Does the diagram give you enough information to show that XWY  ZWY by SSS? W Given: Y is the midpoint of XZ X Z Y Side-Angle-Side Congruence Postulate (SAS) If two ________________ and the ___________________ _______________ of one triangle are ___________________ to two _________________ and the _____________________ _________________ of another triangle, then the triangles are ________________________. If Side _____________, and Angle _____________, and Side ______________, then ___________________. Example: Do you have enough information to show that JLK  MPO by SAS? L M O K P J Example: The two triangles can be proved congruent. State what two triangles are congruent and the reason why. WXY  _________ by ___________ Z W X Y T Angle-Side-Angle Congruence Postulate (ASA) If two ______________ and the ___________________ ______________ of one triangle are ___________________ to two ________________ and the _____________________ ______________ of another triangle, then the triangles are ______________________. If Angle ____________, and Side ______________, and Angle ______________, then __________________. Example: Can you determine that the two triangles are congruent by ASA? If so, name the two congruent triangles. N R T S P O Example: Can you determine that the two triangles are congruent by ASA? If so, name the two congruent triangles. K G H J M L Does the side always need to be between the angles for the triangles to be congruent? Angle-Angle-Side Congruence Theorem (AAS) If two _____________ and a _________________________ ____________ of one triangle are __________________ to two ______________ and a ___________________________ _______________ of another triangle, then the triangles are ______________________. If Angle _____________, and Angle _____________, and Side _______________, then _________________. Example: Can you show that two triangles are congruent by AAS? If so, state the congruent triangles. A B Angle-Side-Side does NOT work (and not just because it spells at bad word!) Right Triangles: Hypotenuse-Leg Congruence Theorem (HL) If the ___________________ and a _____________ of a ________________ triangle are congruent to the ___________________ and a ____________ of a second ________________ triangle, then the two triangles are _____________________. If ________________ are __________ triangles and H ________, and L _________, then ________________. Example: Is it possible to show that the two triangles are congruent by HL? If so, which triangles are congruent? A B D C Example: Is it possible to show that the two triangles are congruent by HL? If so, which triangles are congruent? G H When can we add markings to a diagram? Pg. 124 #4-9 Pg. 124 (bottom) #1-15 Pg. 142 #1-9