In a rectangle ABCD, E is a point which bisects BC Prove that AE = ED

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(a)

In the given figure, if AB = FE, BC=ED, \(AB\bot BD\) and \(FE\bot EC\), then prove that
(i) \(\triangle ABD\cong \triangle FEC\)
(ii) \(AD\cong FC\)

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(a)

Prove that the medians of an equilateral triangle are equal.

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(a)

In the given figure \(BL\bot AC,MC\bot LN\), AL = CN and BL = CM. Prove  that \(\triangle ABC\cong \triangle NML\)

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(a)

In the figure below, ABC is a triangle in which AB = AC. X and Yare points on AB and AC such that AX = AY. Prove that \(\triangle ABY\cong \triangle ACX\) .

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(a)

In the figure, AD = AE, BD = EC. Prove that \(\triangle\)ABC is an isosceles triangle.

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(a)

In \(\triangle\)ABC, if AB is the greatest side, then prove that LC > 60°.

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(a)

For spreading the message "Save Girl Child Save Future" a rally was organized by some students of a school. They were given triangular cardboard piece PQR which they divided in to two parts by drawing the angle bisectors QO and RO of base angles Q and R and wrote a slogan. Prove that \(\angle\)QOR = 90° + \(\frac{1}{2}\)\(\angle\)P. What is the benefit of these types of rallies?

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(a)

I and m are two parallel equal lines intersected by another pair of parallel lines p and q (see figure) :

(i) Show that \(\triangle ABC\cong \triangle CDA\)
(ii) Which mathematical concept is used in this problem?
(iii) What is its value?

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(a)

AD and BC are equal perpendiculars to a line segment AB (see figure).

(i) Show that CD bisects AB.
(ii) Which mathematical concept is used in this problem?
(iii) What is its value?

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(a)