# Triangles - Class 9 - Mathematics

Renews every month. Cancel anytime

### Your personal doubt-solving assistant

Chatterbot AI gives you 100% accurate answers to your questions in an instant.

## Extra Questions - Triangles | NCERT | Mathematics | Class 9

How many triangles can be drawn having its angles as $53^{\circ}, 64^{\circ}$, and $63^{\circ}$?

A) A Unique triangle

B) Two triangles

C) Infinitely many triangles

D) None of these

The correct answer is **C. Infinitely many triangles**

We start by calculating the sum of the given angles:
$$
53^{\circ} + 64^{\circ} + 63^{\circ} = 180^{\circ}
$$
Since the sum of the angles is **$180^{\circ}$**, which is the required sum for the angles of any triangle, we conclude that a triangle with these angles can indeed exist.

Furthermore, as these angle measures do not depend on the side lengths, and since triangle sides can vary while maintaining the same angle measures (by the property of similar triangles), **infinitely many triangles** can be constructed. These triangles will be similar in shape but can differ in size, leading to the conclusion that option **C** is correct.

The midpoints of an equilateral triangle of side $10 \mathrm{~cm}$ are joined to form a triangle. What type of triangle is obtained by joining the midpoints?

A. Equilateral triangle of side $5 \sqrt{3} \mathrm{~cm}$

B. Isosceles triangle, in which the equal sides measure $5 \sqrt{2} \mathrm{~cm}$

C. Isosceles triangle, in which the unequal side measures $5 \sqrt{2} \mathrm{~cm}$

D. Equilateral triangle of side $5 \mathrm{~cm}$

### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

Join English Chatterbox to access detailed and curated answers, and score higher than you ever have in your exams.

Sign up now### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

### Improve your grades!

In a triangle, the centroid is the point of intersection of:

A) altitudes.

B) perpendicular bisectors.

C) medians.

D) angular bisectors.