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t4trendesetter | (Level 1) Honors

Posted March 25, 2013 at 6:52 PM via web

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I really need help on this question that i'm stuck on. I'll really appreciate it!

Write a proof that line AC is congruent to BD.

             Statements                                Reasons

                     ?                                            ?

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quirozd | High School Teacher | (Level 3) Adjunct Educator

Posted March 25, 2013 at 7:35 PM (Answer #2)

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Based on your image:

Concepts Alternate Interior Angles Converse, Reflexive Property, Parallelograms or Triangle Congruency.

Remember to state your givens and definitions, you need to build up the step-by-step logical case that AC is congruent to BD.

Solution using Parallelograms

angles CBA and DAB are congruent - Given

angles CAB and DBA are right angles (and congruent) - Given

angles CBA and DAB are alternate interior angles - Definition

segments BC and AD are parallel - alternate interior angles converse

angles CAB and DBA are alternate interior angles - Definition

segments AC and BD are parallel - alternate interior angles

(ACBD is a quadrilateral - definition)

ACBD is a parallelogram - Parallelogram Converse

AC is congruent to BD - ACBD is a parallelogram, opposite sides are congruent.

ALTERNATE solution - using ASA Triangle Congruency

Once you have identified congruence of the angles (see above)... 

AB is congruent to BA - reflexive property

Triangles ABD and BAC are congruent - Angle-Side-Angle Congruency

AC is congruent to BD - CPCTC: Corresponding parts of congruent triangles are congruent.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 27, 2013 at 9:18 AM (Answer #3)

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In triangle CAB    and   triangle DBA

angle CAB   =   angle DBA          (given)

           AB   =   BA                  (same line )

 angle ABC  =    angle BAD        (given)

There fore     triangle CAB congruence to triangle DBA    by ASA .

 Thus       AC=BD     ( congruent part of congruent triangle) 

 

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