Free download NCERT Solutions for Class 9 Maths Chapter 7 triangles exercise 7.1, 7.2, 7.3, 7.4 and 7.5 in PDF form with other chapters of class 9 maths solutions. NCERT books in ZIP format or NCERT books in PDF format are also given to download.

## NCERT Solutions for Class 9 Maths Chapter 7

### Class 9 Maths Chapter 7 – Important Questions

#### Triangles – Questions with answers

- If ∆ABC is an isosceles triangle such that AB = AC, then prove that altitude AD from A on BC bisects it.
- In a ∆PQR, angle P = 110°, PQ = PR. Find angle Q and angle R. [Answer: angle Q = 35 and angle R = 35]
- In ∆ABC, if angle A = 55°, angle B = 75° then find out the smallest and longest side of the triangle. [Answer: Smallest = AB, Longest = AC]
- The vertex angle of an isosceles triangle is 80°. Find out the measure of base angles. [Answer: 50, 50]
- ABC is a triangle and D is the mid-point of BC. The perpendicular from D to AB and AC are equal. Prove that triangle is isosceles.
- Prove that angles opposite to the equal sides of an isosceles triangle are equal.
- S is any point in the interior of a ∆PQR. Prove that SQ + SR < PQ + PR.
- In ∆DEF, angle E = 2angle F. DM is the angle bisector of angle EDF that intersects EF at M. If DM = MF, then prove that angle EDF = 72°.
- Prove that the angles of an equilateral triangle are 60° each.
- AF, BD and CE are altitudes of ∆ABC are equal. Prove that ∆ABC is an equilateral triangle.
- Prove that two triangles are congruent if two angles and the included side of one triangle are equal to the two angles and the included side of the other triangle.
- O is any point in the interior of a ∆ABC. Prove that OA + OB + OC > 1/2 (AB + BC + CA).
- Prove that the perimeter of a triangle is greater than the sum of its three altitudes.
- Two sides AB, BC and median AM of ∆ABC are respectively equal to sides PQ, QR and median PN of ∆PQR. Show that: ∆ABM and ∆PQN are congruent.
- Ram has a land in the shape of a square PQRS. Its diagonals PR and QS intersect at O. Show that ∆POQ, ∆QOR, ∆ROS and ∆SOP are congruent. Ram donates two triangular parts of land for opening a hospital and a school. Which values are exhibited by Ram? [Answer: Charity, Care for society]