1.

Solve the following (Any One) : If a line is drawn parallel to one side of a triangle and intersects the other two sides, then the other two sides are divided in the same ratio. OR In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. ​

Answer» ONG>Answer:

if a line is drawn parallel to ONE side of a triangle to intersect the other TWO SIDES in distinct points, the other two sides are divided in the same ratio. If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the THIRD side.

Step-by-step explanation:

ANSWER

Given:- ABC is a triangle

AC

2

=AB

2

+BC

2

To prove:- ∠B=90°

Construction:- Construct a triangle PQR right angled at Q such that, PQ=AB and QR=BC

Proof:-

In △PQR

PR

2

=PQ

2

+QR

2

(By pythagoras theorem)

⇒PR

2

=AB

2

+BC

2

.....(1)(∵AB=PQ and QR=BC)

AC

2

=AB

2

+BC

2

.....(2)(Given)

From equation (1)&(2), we have

AC

2

=PR

2

⇒AC=PR.....(3)

Now, in △ABC and △PQR

AB=PQ

BC=QR

AC=PR(From (3))

∴△ABC≅△PQR(By SSS congruency)

Therefore, by C.P.C.T.,

∠B=∠Q

∵∠Q=90°

∴∠B=90°

Hence proved.


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