Q.1. In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that :

(i) OB = OC

(ii) AO bisects ∠ A

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Q.2. In Δ ABC, AD is the perpendicular bisector of BC (see Figure). Show that Δ 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 (see Figure). 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 (see Figure). Show that

(i) Δ ABE ≅ Δ 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 (see Figure). Show that ∠ ABD = ∠ ACD.

Q.6. ΔABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Figure). Show that ∠ BCD is a right angle.

Q.7. ABC is a right angled triangle in which ∠ A = 90° and AB = AC. Find ∠ B and ∠ C.

Q.8. Show that the angles of an equilateral triangle are 60° each.

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NCERT Solutions For Class 9 Maths Chapter 7, Triangles (All Exercises)