NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.4

NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.4 (Ex. 10.4) Practical Geometry in Hindi and English Medium updated for academic session 2021-2022. All the contents and solutions are updated according to latest NCERT Books issued for 2021-22.

In exercise 10.4 of class vii, we have to study the method of construction triangles, when two angles and one side is given. There are only 3 questions in exercise 10.3 and all the easy to solve.

Class 7 Maths Chapter 10 Exercise 10.4 Solution




Class: 7Mathematics
Chapter: 10Practical Geometry
Exercise: 10.4NCERT Book’s Solution

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ll. SAS (Two sides and included angle) Triangle Construction

To construct a triangle when two of its sides and the included angle are given.
Example:
Construct a triangle ABC in which AB = 5 cm, AC = 4.3 cm and ∠A = 600. Also, draw the perpendicular bisector of BC.
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 AB = 5 cm.
2. Construct ∠BAX = 60°.
3. Along AX, set off AC = 4.3 cm.
4. Join BC. Then, triangle ABC is the required triangle.
5. With B as centre and radius measuring more than half of BC, draw arcs on both sides of BC.
6. With C as centre and the same radius as before, draw arcs on both sides of BC, cutting the previous arcs at P and Q, as shown, Join PQ.

Then, triangle ABC is required triangle.

Class 7 Maths Exercise 10.4 Important Questions

Can a triangle have two obtuse angles?

The answer is “No”. Reason: If a triangle has two obtuse angles, then the sum of all the 3 interior angles will not be equal to 180 degrees.

Which is the longest side of a right triangle?

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.

Can there be two right angles in a triangle?

No, a triangle can never have two right angles. A triangle has exactly 3 sides and the sum of interior angles is 180°. Thus, it is not possible to have a triangle with 2 right angles.

Construct a triangle PQR in which QR = 4.2 cm, ∠Q = 120° and PQ = 3.5 cm. Draw PM Ʇ QR.

Construction:
First we draw a rough sketch of triangle PQR. Then, we construct triangle PQR in following steps:
Steps of construction:
1. Draw a line segment QR = 4.2cm.
2. Construct ÐRQX = 120°.
3. Along QX, set off QR = 3.5 cm.
4. Join PR. Then, DPQR is the required triangle.
5. Produce RQ to S to the left.
6. With P as centre and with a sufficient radius, draw an arc, cutting SQ at A and B.
7. With A as centre and radius more than half of AB, draw an arc. Now with B as centre and with the same radius draw another arc, cutting the previous arc at C.
8. Join PC, meeting RQ produced at M. Then, PM Ʇ QR

NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.4