Construct a square with diagonal 6 cm without using a protractor. Class 8

Construct a square with diagonal 6 cm without using a protractor. Class 8

Question 1.

Construct a square with diagonal 6 cm without using a protractor. Class 8

Solution:

Step 1. Draw a line segment AB = 6 cm.

Step 2. Draw the perpendicular bisector XY of AB, using ruler and compass intersecting AB at M.

Step 3. With M as centre and AM (= 3 cm) as radius, draw arcs to intersect XY at C and D.

Step 4. Join AC, BC, BD and AD.

Then, ACBD is the required square

Question 2.

If a quadrilateral has four equal sides and one angle of 90°, will it be a square? Find the answer using geometric reasoning as well as by construction and measurement. Class 8

Solution:

Yes, it will be a square.

Because, this quadrilateral is a rhombus also.

So, ∠A = ∠C = 90°.

Also, ∠D = ∠B = 180° - 90° = 90° (AD || BC)

Hence, a square.

Note : Verify it by construction also.