Question

In triangle ABC, where AB is perpendicular to BC, AD = BC, and angle ABC = 90°, what is the condition for AD to be equal to BD? a) AD = BD if angle CAD = angle CBA b) AD = BD if angle ADB = angle BCA c) AD = BD if angle ADC = angle BCA d) AD = BD if angle ACB = angle CAD

Answer 1

The condition for AD to be equal to BD in triangle ABC is when angle ADC = angle BCA.

Step-by-step explanation:

The condition for AD to be equal to BD in triangle ABC is option c) AD = BD if angle ADC = angle BCA.

Since AB is perpendicular to BC, angle ABC is a right angle, which means it measures 90°. If AD and BD are equal in length, it implies that AD and BD are both radii of a circle centered at the midpoint of AB.

This means that angle ADC, which is an inscribed angle, is equal to angle BCA, which is the central angle of the same arc AD and DB.

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