RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions

RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions is based on the topics like- Useful Facts about Triangles and Theorems Result of Triangles.

Some important results-

• The line segment connecting the mid-points of any two sides of a triangle is parallel to the third and equivalent to half of it.
• The line formed through the mid-point of one side of a triangle, parallel to the other side, crosses the third side at its mid-point.

We have given the RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions PDF for more understanding about the exercise. In this PDF, various types of questions are there with complete stepwise explanations and examples. Go down to the article and know about the facts about the triangle and the result of the theorem with explanations and examples.

Download RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions PDF

Solutions for Class 9 Maths Chapter 14 Quadrilaterals Exercise 14.4

Important Definitions RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions

Here are some significant results of the theorems of triangles-

1. The line segment connecting the mid-points of any two sides of a triangle is parallel to the third and equivalent to half of it.
2. The line formed through the mid-point of one side of a triangle, parallel to the other side, crosses the third side at its mid-point.

Examples of RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions

Ques 1- In a ΔLMN, O, P, and Q are, respectively, the midpoints of MN, NL, and LM. If the lengths of sides LM, MN, and NL are 7 cm, 8 cm, and 9 cm, respectively, find the perimeter of ΔOPQ.

Solution-

Given: LM = 7 cm, MN = 8 cm, LN = 9 cm

In ∆LMN,

In a ΔLMN, O, P, and Q are, respectively, the midpoints of MN, NL, and LM.

According to Midpoint Theorem: OP= 1/2 LM

Now, Perimeter of ∆OPQ = OP + PQ + OQ

= 1/2 (LM + MN + NL)

= 1/2 (7 + 8 + 9)

= 12

Ques 2- In a ΔLMN, ∠L = 50°, ∠M = 60° and ∠N = 70°. Obtain the measures of the angles of the triangle formed by joining the mid-points of the sides of this triangle. Solution-

In ΔLMN,

Triangle LMNO and P are midpoints of LM and MN.

By Midpoint theorem,

NO ∥ LN, OP = (1/2) LM

Q is the midpoint of LN

Then, OP = (1/2) LN = NQ

OP ∥ LN, OP = NQ

Hence OPNQ is a parallelogram.

Therefore, ∠N = ∠O = 70° [Opposite sides of a parallelogram]

Similarly

MPQO is a parallelogram, ∠M = ∠Q = 60°

LOPQ is a parallelogram, ∠L = ∠P = 50°

Therefore, Angles of ΔOPQ are

∠O = 70°, ∠P = 50°, ∠Q = 60°

Frequently Asked Questions (FAQs) of RD Sharma Chapter 14 Class 9 Maths Exercise 14.4 Solutions

Ques 1- How many triangles make a quadrilateral?

Ans- Two triangles make a quadrilateral. As the total of the interior angles of any triangle is 180° (180 degrees) and there are two (2) triangles in a quadrilateral, the whole of the angles for each quadrilateral is 360° (360 degrees).

Ques 2- What makes a shape a quadrilateral?

Ans- A quadrilateral is a polygon that has specifically four sides/ edges. (This also signifies that a quadrilateral has specifically four vertices and four angles.)