ABCD is a quadrilateral such that diagonal AC bisects the angles ∠A and ∠C. Prove that AB = AD and CB = CD.
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Answer:
Step-by-step explanation:
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.
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Read more on Brainly.in - https://brainly.in/question/3868163#readmoreAC 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.