# NCERT Solutions for Class 9 Maths Chapter 7

Free download NCERT Solutions for Class 9 Maths Chapter 7 triangles exercise 7.1, 7.2, 7.3, 7.4 and 7.5 in English Medium and Hindi Medium free to use online 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

If you need solutions in Hindi, Click for Hindi Medium solutions of 9 Maths Chapter 7           Previous Chapter: Chapter 6

9 Maths Solutions: Main Page

Next Chapter: Chapter 8

### 9 Maths Chapter 7 All Exercises in Hindi           Previous Chapter: Chapter 6

9 Maths Solutions: Main Page

Next Chapter: Chapter 8

To get the solutions in English, Click for English Medium solutions.

##### Class 9 Maths Chapter 7 – Important Questions
###### Triangles – Questions with answers
1.  If ∆ABC is an isosceles triangle such that AB = AC, then prove that altitude AD from A on BC bisects it.
2. In a ∆PQR, angle P = 110°, PQ = PR. Find angle Q and angle R. [Answer: angle Q = 35 and angle R = 35]
3. 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]
4. The vertex angle of an isosceles triangle is 80°. Find out the measure of base angles. [Answer: 50, 50]
5. 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.
6. Prove that angles opposite to the equal sides of an isosceles triangle are equal.
7. S is any point in the interior of a ∆PQR. Prove that SQ + SR < PQ + PR.
8. 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°.
9. Prove that the angles of an equilateral triangle are 60° each.
10. AF, BD and CE are altitudes of ∆ABC are equal. Prove that ∆ABC is an equilateral triangle.
11. 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.
12. O is any point in the interior of a ∆ABC. Prove that OA + OB + OC > 1/2 (AB + BC + CA).
13. Prove that the perimeter of a triangle is greater than the sum of its three altitudes.
14. 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.
15. 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]