CBSE Class 10-Mathematics: Chapter – 6 Triangles Part 19 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 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

Prove That in a Right-Angled Triangle

Answer:

Given: right-angled at A

To Prove:

Construction: Draw from A to BC

Proof: In

Similarly, in

To prove

Proof: In

Question 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 , if the largest side of the smaller triangle is 27 cm, then find the largest side of the largest triangle.

Area of Two Similar Triangles

Answer:

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

From (i) and (ii) , we get

Now

Hence,

Let the largest side of the largest triangle be

Using above theorem,

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