CBSE Class 9 Maths Properties of Isosceles Triangle
 M is a point inside a square ABCD. AMCD is equilateral triangle and MC cuts diagonal DB at E. Then, ZBEC=..... (1) 75° (3) 105° (2) 90° (4) 60°
 In fig. 12.116 , T is a point on the side QR of ∆ PQR and S is a point such that RT=St. Prove that PQ+PR>QS
 In the figure, ABCD is a square and PAB is a triangle such that AQ = BR. Prove that DPQR is an isosceles triangle.
 If the vertex angle of an isosceles triangle is 50° ,find the other angels

show that BX=CY.
 AD is an altitude of an isosceles triangle ABC in which AB=AC.Show that ( i )AD bisects BC (ii) AD bisects angle A.
 If the segments drawn perpendicular to the two sides of a triangle from the mid point of the third side be congruent and equally inclined to the third side, prove that the triangle is isosceles.
 If the altitudes from two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.