# NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.5

Do you need NCERT Solutions for Class 9 Maths Chapter 7 Exercise 7.5 Triangles? Ex. 7.5 of class 9 Maths is an optional exercise, but questions may also be asked from this exercise.

The complete exercise 7.5 is given here in PDF file format to use it offline, but online users can use it without downloading. Videos related to exercise 7.5 in Hindi and English Medium are also given here to practice well for exams.

## Class 9 Maths Exercise 7.5 Solution in Hindi and English Medium

 Class: 9 Mathematics Chapter: 7 Triangles Exercise: 7.5 NCERT Solutions in PDF and Videos

### Class 9 Maths Exercise 7.5 Solution in Hindi Medium Video

#### Class 9 Maths Chapter 7 Exercise 7.5 Solution in Videos

Class 9 Maths Exercise 7.5 Question 1 and 2
Class 9 Maths Exercise 7.5 Question 3 and 4

#### Class 9 Maths Chapter 7 Exercise 7.5 Solution

##### Is exercise 7.5 considered as an optional exercise?

Yes, there may not be any question from this exercise in the exams.

##### Why should we do the optional exercise 7.5?

Optional exercises provide some extra tricky questions based on the main concepts of the chapter.

##### What is the deleted portion from chapter 7 of class 9 Maths due to COVID-19?

The proof of theorem ASA is now deleted from the course, and questions based on inequalities and relation between angle and facing side inequality in triangle also deleted for session 2020-2021.

##### Important Points to be remembered
1. Two shapes converge if they have the same shape and size.
2. Two circles of the same radius are congruent.
3. Two squares with the same side are congruent.
4. If two triangles ABC and PQR correspond under the correspondence A, P, B ↔ Q and C and R, Mathematically, it is expressed as ΔABC ≅ ΔPQR.
5. If the two angles of a triangle and the triangle are equal to the two sides and the other triangle angles are equal, then the two triangles are congruent (SAS Rule).

## Solution of Example 1 Class 9 Maths In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD = AE. Solution: In Δ ABD and Δ ACE, AB = AC (Given in the question) … (1) ∠ B = ∠ C (We know that the angles opposite to equal sides) … (2) It is also given that, BE = CD So, we have BE – DE = CD – DE Finally, we get, BD = CE … (3) So, Δ ABD ≅ Δ ACE (Using (1), (2), (3) and SAS rule). So, we get AD = AE (CPCT)

## Class 9 Maths Practice Question 2 Solution In Δ ABC, the bisector AD of ∠ A is perpendicular to side BC. Show that AB = AC and Δ ABC is isosceles. Solution: In ΔABD and ΔACD, ∠ BAD = ∠ CAD (Given) AD = AD (Common) ∠ ADB = ∠ ADC = 90° (Given) So, Δ ABD ≅ Δ ACD (ASA rule) So, AB = AC (CPCT) or, Δ ABC is an isosceles triangle.  