2VocabularyIn a right triangle, the sides adjacent to the right angle are the legs.The side opposite the right angle is the hypotenuse.Side-Angle-Side (SAS) Congruence Postulate: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the two triangles are congruent.
3Is there enough given information to prove the triangles congruent Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.1.ABE, CBDANSWERSAS Post.
4State a third congruence that would allow you to prove RST XYZ by the SAS Congruence postulate. 3.ST YZ, RS XYANSWERS Y.
5EXAMPLE 1Use the SAS Congruence PostulateWrite a proof.GIVENBC DA, BC ADPROVEABC CDASTATEMENTSREASONSGivenBC DASGivenBC ADBCA DACAlternate Interior Angles TheoremAAC CAReflexive Property of CongruenceSABC CDA5. SAS
7Hypotenuse-Leg (HL) Congruence Theorem – If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, the triangles are congruent.
8Tell whether the pair of triangles is congruent or not and why. ANSWERYes; HL Thm.
9Is there enough given information to prove the triangles congruent Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem.2.FGH, HJKANSWERHL Thm.
10EXAMPLE 3Use the Hypotenuse-Leg Congruence TheoremWrite a proof.GIVENWY XZ, WZ ZY, XY ZYPROVEWYZ XZYSOLUTIONRedraw the triangles so they are side by side with corresponding parts in the same position. Mark the given information in the diagram.
11EXAMPLE 3Use the Hypotenuse-Leg Congruence TheoremSTATEMENTSREASONSWY XZGivenWZ ZY, XY ZYGivenDefinition of linesZ and Y are right anglesDefinition of a right triangleWYZ and XZY are right triangles.LZY YZReflexive Property of CongruenceWYZ XZYHL Congruence Theorem
12Extra Practice Complete in your notebooks. Page ,22, 31, 32, 34