NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.5 (Ex. 10.5) Practical Geometry free to use online or download in PDF file format for session 2022-2023. All the contents are updated for session 2022-23 following the latest CBSE curriculum 2022-2023. In class 7 math ex. 10.5 we will study about the construction of right angled triangle. Only three questions are given in exercise 10.5 of class vii math. All questions need more practice to learn better.

## Class 7 Maths Chapter 10 Exercise 10.5 Solution

### CBSE NCERT Class 7 Maths Chapter 10 Exercise 10.5 Solution in Hindi and English Medium

Class: 7 | Mathematics |

Chapter: 10 | Practical Geometry |

Exercise: 10.5 | NCERT Textbook Solution |

### Class 7 Maths Chapter 10 Exercise 10.5 Solution in Videos

#### lll. ASA Triangle Construction

Example:

Construct a triangle ABC in which BC = 4.8 cm, âˆ B = 60Â° and âˆ C = 75Â°.

Construction: First we draw a rough sketch of triangle ABC. Then, we draw triangle ABC in following steps.

Steps of construction:

1. Draw a line segment BC = 4.8 cm.

2. Construct âˆ CBX = 60Â° and âˆ BCY = 75Â°.

3. Let BX and CY intersect at A.

Then, triangle ABC is the required triangle.

##### Right-Angled Triangle

A triangle ABC is said to be right-angled at B, if âˆ B = 90Â°.

In this case, AC is called the hypotenuse of triangle ABC.

##### IV. RHS (Right angle hypotenuse and one side) Triangle Construction

To construct a right triangle when its hypotenuse and one side are given.

Example:

Construct a triangle ABC in which base BC = 4.8 cm, âˆ B = 90Â° and hypotenuse AC = 6.2 cm.

Construction:

First we draw a rough sketch of triangle ABC, then, we draw triangle ABC in following steps.

Steps of construction:

1. Draw a line segment BC = 4.8 cm.

2. Construct âˆ CBX =90Â°.

3. With C as centre and with radius 6.2 cm, draw an arc, cutting BX at A.

4. Join AC

Then, triangle ABC is the required triangle.

### Class 7 Maths Exercise 10.5 Important Questions

### How many obtuse angles do triangles have?

An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90Â°) and two acute angles. Since a triangle’s angles must sum to 180Â° in Euclidean geometry, no Euclidean triangle can have more than one obtuse angle.

### Does 9 cm, 12 cm and 15 cm make a right triangle?

The three sides 9 in, 12 in, and 15 in do represent a right triangle. Since the square of the hypotenuse is equal to the sum of the squares of the other two sides, this is a right triangle.

### Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the sides is 5 cm long.

First we draw a rough sketch.

Steps of construction:

1. Draw a line segment AB = 5 cm.

2. At B, draw âˆ ABX = 90Â°.

### Construct a Triangle ABC in which BC = 5.3 cm, âˆ B = 45Â° and âˆ A = 75Â°.

We know that the sum of the angles of a triangle is 180Â°.

So, âˆ A + âˆ B + âˆ C = 180Â°

Or, 75Â° + 45Â° + âˆ C = 180Â°.

Or, âˆ C = 180Â° – 120Â° = 60Â°.

Thus, we have: BC = 5.3 cm,

Or, âˆ B = 45Â° and âˆ C = 60Â°.

First we draw a rough sketch of triangle ABC, as shown.

Steps of construction:

1. Draw a line segment BC = 5.3 cm.

2. Construct âˆ CBX = 45Â° and âˆ BCY = 60Â°.

3. Let BX and CY intersect at A.

Then, triangle ABC is the required triangle.