Questions: Given: AC is the perpendicular bisector of BD Prove: angle 1 is congruent to angle 2

Transcript text: Given: $\overline{A C}$ is the perpendicular bisector of $\overline{B D}$ Prove: $\angle 1 \cong \angle 2$

Solution

Step 1: Using the definition of Perpendicular Bisector

AC is the perpendicular bisector of BD, therefore ED is congruent to EB.

Step 2: Using the Perpendicular Bisector Theorem

Any point on the perpendicular bisector is equidistant from the endpoints of the segment it bisects. So, CD is congruent to CB.

Step 3: Using the reflexive property of congruence

CA is congruent to itself.

Step 4: Using Side-Side-Side (SSS) Postulate

Triangle CDA is congruent to triangle CBA by the SSS postulate.

Step 5: Congruent Triangles have Congruent Corresponding Parts

Since triangle CDA is congruent to triangle CBA, their corresponding parts are congruent, therefore angle 1 is congruent to angle 2.

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