Prove that the angle inscribed in a semi-circle is a right angle.
1 Answer
Given: O is the center of the circle, AB is diameter and ACB is an angle inscribed in a semi-circle.
To prove: ACB = 90°
| S.N | Statements | Reasons |
| 1 | ACB = 1/2 AOB | ACB is a circumference angle and AOB is a central angle standing on the same arc as ADB. |
| 2 | AOB = 180° | A straight angle. |
| 3 | ACB = (1/2)*180 = 90° | From statements (1) and (2), by substitution axiom |
| 4 | Therefore, ACB is a right angle. | From statement 3. |
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