Question

$△$XYZ is constructed such that XY = 8.5 cm, YZ = 5.5 cm and $\angle$Y = 40${}^{\circ }$. Then $△$XYZ is an isosceles triangle.

• A. True
• B. False

Answer 1

The correct option is A

True

Step 1:
Draw the base line XY of the length 8.5 cm.

Step 2:
Measure the angle Y with your protractor. Make a mark at 40 degrees and draw a line from Y passing through the mark.

Step 3:
Cut an arc of radius 5.5 cm on the line passing through the point Y. The point where this arc cuts the line is the point Z.

Step 4:
Draw a line from X to point Z, to get the required triangle XYZ, as shown below.

From the above construction, we see that the length of side XZ is 5.5 cm, which is equal to the length of side YZ.

Hence it is true that $△$XYZ is an isosceles triangle.