Diagonals of Rectangles and Squares

Class 6 Maths · Chapter 8: Playing with Constructions · NCERT Ganita Prakash section 8.5

Learn

A line joining opposite corners is a diagonal. A rectangle ABCD has two: AC and BD. Nisha measures both on her notebook cover: 25 cm and 25 cm. The two diagonals of a rectangle are always equal.

The diagonals cross at a point O in the middle. O cuts each diagonal in half: OA = OC and OB = OD. So all four, OA, OB, OC and OD, are equal!

OA = OB = OC = OD

That gives a neat construction: draw two equal lines that cut each other in half, and join their ends. You always get a rectangle! It is also how to construct a rectangle from one side and a diagonal.

In a square, the diagonals do one more thing: they cross at a right angle (90°). In a long thin rectangle they cross at a slant.

Explore: change the rectangle and watch its diagonals.

1. Make a rectangle 8 cm by 6 cm. How long is each diagonal?
2. Make the diagonals cross at a right angle.
3. Make a rectangle whose diagonals are 5 cm long.

Remember

• The diagonals of a rectangle are equal and cut each other in half.
• The diagonals of a square also cross at 90°.

Quick check

In rectangle PQRS the diagonals cross at O, and PR = 12 cm. How long is OQ?

1. 6 cm
2. 12 cm
3. 24 cm
4. 3 cm

Think about it

Rohan draws two lines, each 6 cm long, that cross at their middle points at 90°. He joins the four ends. What shape does he get?

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.