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Chapter 5: Q31 (page 188)

Given: Rectangle QRST; 鈻�RKST; 鈻�JQST

Prove: JT炉鈮�KS炉.

Short Answer

Expert verified

JT炉鈮�KS炉

Step by step solution

01

Step 1. State the concept used.

Diagonals of rectangles are equal and bisect each other.

The opposite sides of a parallelogram are equal.

02

Step 2. State the proof.

Construct a rectangle QRSTand parallelogram 鈻�RKSTwith parallelogram 鈻�JQST.

In parallelogram 鈻�RKST, RTand SKare opposite sides which are parallel,

Therefore, RT炉鈮�SK炉

Similarly, in parallelogram 鈻�JQST, JTand QSare opposite sides which are parallel,

Therefore, JT炉鈮�QS炉.

Now, in rectangle QRST, TRand QSare diagonal of the rectangle and as the diagonal of the rectangle are equal to each other, it can be said that, TR炉鈮�QS炉.

From the above three relations by the property of transitivity of congruence, JT炉鈮�KS炉.

Hence, JT炉鈮�KS炉.

03

Step 3. State the conclusion.

Therefore, JT炉鈮�KS炉(proved).

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