2020 · Q61
In a quadrilateral ABCD, ∠B = 90° and AB² + BC² + CD² − AD² = 0, then what is ∠ACD equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A30°
- B60°
- C90°
- D120°
Explanation
AB^2+BC^2 = AC^2 since angle B is 90 degrees; the given condition then yields AD^2 = AC^2+CD^2, so angle ACD = 90 degrees. Hence option (C). In particular AD^2 = AC^2+CD^2 is the converse of Pythagoras applied to triangle ACD.