In triangle ABC, AM is the bisector of angle BAC. MP is drawn perpendicular to AB and MQ is perpendicular to AC.
a) Prove that MP,and MQ are of the same length.
b) Prove that, in any triangle, the bisector of an angle divides the oppositè sidein the ratio of the sides of the angle.

Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

In triangle 'ABC, angle B=90 degree and 'BD' is perpendicular to AC. a) If 'angle A=x degree, write the angles of triangles 'ABD' 'and 'BDC'. b) Prove that '(BD)^2=AD X CD'.

The perpendicular from the square comers of a right triangle cuts the opposite side into two parts of 2 and 3 cm length. Prove that if the perpendicular from the square corner of the right triangle divides the opposite sides into partsof length a and b and if the length of the perpendicular is h, then h^2= ab .

In triangle ABC, AB=14 cm, AC=15cm, sin A=4/5 . Find the following: a) The perpendicular distance from C to AB. b) The area of the triangle. c) The length of BC.

The perpendicular sides of a right angled triangle are 12 and 15 centimetres long. Another right angled triangle of the same area has one of the perpendicular sides 18 centimetres long. What is the length of the other?

The perpendicular from the square corners of a right angle triangle cuts the opposite side into two parts of 2 and 3 cm length. Calculate the perpendicular sides of the large triangle.