# Important Questions for CBSE Class 10 Maths Chapter 6 - Triangles 4 Mark Question

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CBSE Class 10 Maths Chapter-6 Triangles Important Questions

## 4 Mark Questions

1. Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in district points, ten other two sides are divided in the same ratio. By using this theorem, prove that in if then

Ans. Given: In intersect AB at D and AC at E.
To Prove:
Construction: Draw and and join DC and BE.
Proof:

Similarly,
Since and are on the same base and between the same parallels

2. Prove that the ratio of areas of two similar triangles are in the ratio of the squares of the corresponding sides. By using the above theorem solve in two similar triangles PQR and LMN, QR = 15cm and MN = 10 cm. Find the ratio of areas of two triangles.

Ans.
Given: Two triangles ABC and DEF
Such that
To Prove:
Construction: Draw and
Proof:

Again, in and we have

[By AA rule]
[Corresponding sides of similar triangles are proportional]
Further,

From (ii) and (iii),

Putting in (i), we get

Hence,
Since

Hence, required ratio is 9:4.

3. Prove that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.Use the above theorem in the given figure to prove that

Ans. Given: right-angled at A
To Prove:
Construction: Draw from A to BC
Proof: In
[Common]

[By AA similarity]

Similarly, in and

[Common]
[By AA similarity]

To Prove:
Proof: In
[Using above theorem]

4. Prove that the ratio of areas of two similar triangles is equal to the square of their corresponding sides.Using the above theorem do the following the area of two similar triangles are and , if the largest side of the smaller triangle is 27 cm, then find the largest side of the largest triangle.

Ans.
Given: Two triangles ABC and DEF such that
To prove:
Construction: Draw and
Proof: Since similar triangles are equiangular and their corresponding sides are proportional

And
In and

[By AA similarity]

From (i) and (ii), we get

Now

Hence,
Let the largest side of the largest triangle be cm
Using above theorem,

5. In a triangle if the square of one side is equal to the sum of the squares on the other two sides. Prove that the angle apposite to the first side is a right angle.Use the above theorem to find the measure of in figure given below.

Ans. Given: A such that

To prove: Triangle ABC is right angled at B
Construction: Construct a triangle DEF such that
andÐ
Proof: is a right angled triangle right angled at E [construction]
By Pythagoras theorem, we have

Thus, in and we have

[By Construction and (i)]

Hence,is a right triangle.
In

Now in
is right angled at K