NCERT Solutions Class 9 Maths Chapter 7 – Triangles Exercise 7.2

Chapter 7 – Triangles Exercise 7.2

(Q 1) In an isosceles triangle ABC, with AB = AC, the bisectors of Ð B and Ð 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 D ABC, AD is the perpendicular bisector of BC (see Fig. 7.30). Show that ∆ ABC is an isosceles triangle in which AB = AC.

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(Q 3) ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see Fig. 7.31). Show that these altitudes are equal

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(Q 4) ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see Fig. 7.32). Show that
(i) ∆ABE ≅ ∆ ACF
(ii) AB = AC, i.e., ABC is an isosceles triangle.

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(Q 5) ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.

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(Q 6) ∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠BCD is a right angle.

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

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

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