Question
The angle inscribed in the semicircle is a right angle. Prove the result by completing the following activity.
Given: $\angle A B C$ is inscribed angle in a semicircle with center $M$
To prove: $\angle A B C$ is a right angle.
Proof: Segment AC is a diameter of the circle.
$
\therefore m(\operatorname{arc} A X C)=\square
$
Arc $A X C$ is intercepted by the inscribed angle $\angle A B C$
$\angle ABC =\square$ [Inscribed angle theorem]
$
=\frac{1}{2} \times \square
$
$\therefore m \angle ABC =\square$
$\therefore \angle ABC$ is a right angle.
Given: $\angle A B C$ is inscribed angle in a semicircle with center $M$
To prove: $\angle A B C$ is a right angle.
Proof: Segment AC is a diameter of the circle.
$
\therefore m(\operatorname{arc} A X C)=\square
$
Arc $A X C$ is intercepted by the inscribed angle $\angle A B C$
$\angle ABC =\square$ [Inscribed angle theorem]
$
=\frac{1}{2} \times \square
$
$\therefore m \angle ABC =\square$
$\therefore \angle ABC$ is a right angle.