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Construction of Rectangles

1. Construct a rectangle in which one of the diagonals divides the opposite angles into
55° and 35°.

Step 1: Start with a rough diagram of possible construction.
D C
55°
35°

35°
55°
A B

Step 2: Draw a line segment AB with an arbitrary length. A B
Step 3: At point B, draw a perpendicular BX Step 4: Put protractor at point A and make ∠BAC
on AB. = 55° where point C lies on BX.

X

A B

Step 5: Now, at point A, draw a perpendicular AY to AB and mark the point D such that
AD = BC, with the help of a compass.
Y X
D C
Quick Check

What would be the measure of an
angle formed between a diagonal
35° and a side of a square?
55°
A B
Thus, ABCD is the required rectangle with ∠CAB = 55° and ∠DAC = 35°.
2. Construct a rectangle where one of its sides is 4 cm and the length of a diagonal is 7 cm.

Step 1: Start with a rough diagram of possible construction.

D C

7 cm

A 4 cm B
Step 2: First draw the base AB of length 4 cm. A 4 cm B

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