# 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.             ...

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 on

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.

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

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)