Prove that each angle of a rectangle is a right angle.

4

(a)

"A diagonal of a parallelogram divides it into two congruent triangles:"  Prove it.

4

(a)

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles.

4

(a)

In triangle, ABC points M and N  on sides AB and AC respectively are taken so that AM = \(1\over2\) AB and AN = \(1\over4\) AC Prove that MN= \(1\over4\)BC

4

(a)

ABCD is a square and on the side DC, an equilateral triangle is constructed. Prove that:
(i) AE = BE
(ii) ㄥDAE=15°

4

(a)

ABCD is a quadrilateral in which the bisectors of ㄥA and ㄥC meet DC produced at Y and BA produced at X respectively. Prove that ㄥX+ㄥY=\(\frac{1}{2}\)(ㄥA+ㄥC)

4

(a)

Show that the bisectors of angles of a parallelogram enclose a rectangle.

4

(a)

Show that the bisectors of angles of a parallelogram form a rectangle

4

(a)

In given fig., AD is the median of ΔABC. E is the mid-point of AD. DG || BF. Prove that AC = 3AF.

4

(a)

In the given figure, D, E and F are the mid-points of the sides AB, BC and CA respectively of ΔABC. Show that ΔABC is divided into four congruent triangles by joining the point D, E and F.

4

(a)