Question

Prove that dt=tc in trapezium ad parralel bc, ot is drawn parallel to ad, with o the midpoint of ab and t a point on dc. Ad//ot//bc

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given:

AC^2 -BC^2 = AB*CD

In a trapezium, opposite sides are parallel and equal

hence, AB = CD

therefore

AC^2 -BC^2 = AB^2

AB^2 +BC^2 = AC^2

hence ABC forms a right angled triangle since it follows pythagoras theorem

Hence Angle ABC = 90 deg

A trapezium with any one angle 90 is a rectangle.

Hence if AC^2 -BC^2 = AB*CD then we can say that trapezium ABCD is a rectangle.