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`        If in a quadrilateral abcd ,ac bisects angle a and c show that ac is perpendicular to bd`
one year ago

```							In quadrilateral ABCD ,     AC and BD are diagonals . So let they intersect at O.     In triangles ABC and ADC,              angle CAB = angle CAD               angle  ACB = angle ACD               AC = AC               Therefore, triangles ABC and ADC are congruent.               NOW,                       AB = AD (corresponding parts of congruent triangles)                      In triangle ABD,                       AB = AD                      So, triangle ABD is isosceles.                       As we know the angle bisector of the vertical angle of an isosceles triangle                         is also the perpendicular bisector of the base.                     So AC intersects BD at right angle.                       so angle AOD = 90o.
```
one year ago
```							In quadrilateral ABCD ,     AC and BD are diagonals . So let they intersect at O.     In triangles ABC and ADC,              angle CAB = angle CAD               angle  ACB = angle ACD               AC = AC               Therefore, triangles ABC and ADC are congruent.               NOW,                       AB = AD (corresponding parts of congruent triangles)                      In triangle ABD,                       AB = AD                      So, triangle ABD is isosceles.                       As we know the angle bisector of the vertical angle of an isosceles triangle                         is also the perpendicular bisector of the base.                     So AC intersects BD at right angle
```
one year ago
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