In a circle AD is a diameter of a circle with center O . If AB is parallel to CD ,probe that AB=CD.
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See diagram.
Look at the two triangles ABD and ACD.
As AB is parallel to CD and AD intersects the two lines AB and CD, the angles marked as x and y are same in two triangles.
angle BAD = angle CDA
angle BDA = angle CAD
hence angle B = angle C.
Now, the two triangles are similar. there is a common side AD for two triangles. Hence all the sides are same.
Hence AB = CD.
Look at the two triangles ABD and ACD.
As AB is parallel to CD and AD intersects the two lines AB and CD, the angles marked as x and y are same in two triangles.
angle BAD = angle CDA
angle BDA = angle CAD
hence angle B = angle C.
Now, the two triangles are similar. there is a common side AD for two triangles. Hence all the sides are same.
Hence AB = CD.
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