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4-6_Congruence_in_Right_Triangles

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					Congruence in Right Triangles
LESSON 4-6

             Additional Examples




                         One student wrote “ CPA        MPA by SAS” for the diagram
                below. Is the student correct? Explain.

                                   The diagram shows the following congruent parts.
                                   CA   MA
                                   CPA      MPA
                                   PA   PA
                                   There are two pairs of congruent sides and one pair of
                                   congruent angles, but the congruent angles are not
                                   included between the corresponding congruent sides.

                                   The triangles are not congruent by the SAS Postulate,
                                   but they are congruent by the HL Theorem.
                                                                              Quick Check


        HELP                                                                GEOMETRY
Congruence in Right Triangles
LESSON 4-6

             Additional Examples




                            XYZ is isosceles. From vertex X, a perpendicular is drawn
                to YZ, intersecting YZ at point M. Explain why XMY         XMZ.




                                                                             Quick Check


        HELP                                                               GEOMETRY
Congruence in Right Triangles
LESSON 4-6

             Additional Examples

                                                                                  Quick Check

                                   Write a two–column proof.
                                   Given: ABC and DCB are right angles, AC         DB
                                   Prove: ABC       DCB

         Statements                          Reasons
         1. ABC and  DCB are            1. Given
            right angles.
         2.    ABC and DCB are            2. Definition of a right triangle
            right triangles.
         3. AC DB                         3. Given
         4. BC CB                         4. Reflexive Property of Congruence
         5.     ABC       DCB             5. If the hypotenuse and a leg of one right
                                             triangle are congruent to the hypotenuse
                                             and a leg of another right triangle, then the
                                             triangles are congruent. (HL Theorem).


        HELP                                                                    GEOMETRY

				
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