Isosceles Triangle Properties Theorems
NCERT Class 9 Maths Exercise 7.2 Solution
Q. 1. In an isosceles triangle ABC with AB = AC, the bisectors of angle B and angle C intersect each other at O. Join A to O. Show that:
(i) OB = OC,
(ii) AO bisects angle A
Q. 2. In triangle ABC, AD is the perpendicular bisector of BC. Show that triangle ABC is an isosceles triangle in which AB = AC.
Q. 3. ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively. Show that these altitudes are equal.
Q. 4. ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show that:
(i) Triangle ABE is congruent to triangle ACF,
(ii) AB = AC i.e. ABC is an isosceles triangle.
Q. 5. ABC and DBC are two isosceles triangles on the same base BC. Show that: Angle ABD = angle ACD.
Q. 6. Triangle ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB. Show that angle BCD is a right angle
Q. 7. ABC is a right angled triangle in which angle A = 90 degree and AB = AC. Find angle B and angle C.
Q. 8. Show that the angles of an equilateral triangle are 60 degree each.
