NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.5

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 2020-2021. All the contents are updated for session 2020-21 following the latest CBSE curriculum 2020-2021.

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

Class: 7Mathematics
Chapter: 10Practical Geometry
Exercise: 10.5NCERT Textbook Solution

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lll. ASA Triangle Construction

Example:
Construct a triangle ABC in which BC = 4.8 cm, ∠B = 60° and ∠C = 75°.
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 ∠CBX = 60° and ∠BCY = 75°.
3. Let BX and CY intersect at A.
Then, triangle ABC is the required triangle.

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

We know that the sum of the angles of a triangle is 180°.
So, ∠A + ∠B + ∠C = 180°
Or, 75° + 45° + ∠C = 180°.
Or, ∠C = 180° – 120° = 60°.
Thus, we have: BC = 5.3 cm,
Or, ∠B = 45° and ∠C = 60°.
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 ∠CBX = 45° and ∠BCY = 60°.
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 ∠B = 90°.
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, ∠B = 90° 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 ∠CBX =90°.
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.



How many obtuse angles do triangles have?

An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle’s angles must sum to 180° 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 ∠ABX = 90°.

7 Maths Chapter 10 Exercise 10.5