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Given that ∠ADB and ∠CDB are right angles, and BD¯¯¯¯¯ bisects ∠B, prove that D is the midpoint of AC¯¯¯¯¯.

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Answer:

Red marking indicate the two objects are congruent by hypothesis.

Green numbers marks the step below:

1. Angles ABD and CBD are congruent by definition of angular bisector;

2. Side DB is in common between the triangles ABD and CBD;

3. Angles ADB and CBD are congruent since they're both right angles.

1,2,3 [tex]\implies[/tex] Triangles ADB and CBD are congruent by ASA, thus corresponding sides are congruent, in particular AD is congruent to CD, which means D is the midpoint of AC (q.e.d.)

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