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

4

(a)

In figure OA = OB, OC = OD and \(\angle AOB=\angle COD\). Prove that AC = BD

4

(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) \(AD\cong FC\)

4

(a)

In figure, \(\angle QPR=\angle PQR\) and M and N are respectively points on sides QR and PR of \(\triangle PQR\) , such that QM = PN. Prove that OP = OQ, where O is the point of intersecting of PM and QN.

4

(a)

Prove that the angles opposite to equal sides of a triangle are equal. Is the converse true?

4

(a)

In the given figure , AE bisects \(\angle DAC\) and,\(\angle B=\angle C\) Prove that \(AE\parallel BC\)

4

(a)

Suppose line segments AB and CD intersect at 0 in such a way that AO = OD and OB = OC. Prove that AC = BD but AC may not be parallel to BD

4

(a)

In Δ Abc, D is the mid-point of BC The perpendiculars from D to AB and AC are equal.Prove that ΔABC is isosceles.

4

(a)

In figure, ΔABD and ΔBCD are isosceles triangles on the same base BD. Prove that ㄥABC = ㄥADC.

4

(a)

AD, BE and CF, the altitudes of \(\triangle\)ABC are equal. Prove that \(\triangle\)ABC is an equilateral triangle.

4

(a)