Question

$\text{Complete the steps to construct a}\text{triangle XYZ in which}\angle Y={45}^{\circ },\angle Z={90}^{\circ }\text{and XY + YZ + ZX = 13 cm.}$

$\text{Steps of construction:}\text{Step 1: Draw a line segment AB=13 cm.}\text{Step 2: At A, construct an angle of}{45}^{\circ }\text{and at B construct an angle of}{90}^{\circ }.\text{Step 3 will be :}$

• A. Draw perpendicular bisection CD of AX to intersect AB at Y.
• B. Join XY and XZ to obtain required triangle XYZ.
• C. Draw perpendicular bisector EF of XB to intersect AB at Z
• D. Bisect these angles. Let bisector of these angles intersect at point X.

Answer 1

The correct option is D Bisect these angles. Let bisector of these angles intersect at point X.

Steps of construction:

Step 1: Draw a line segment AB=13 cm.

Step 2: At A, construct an angle of ${45}^{\circ }$ and at B construct an angle of ${90}^{\circ }.$

Step 3: Bisect these angles. Let bisector of these angles intersect at point X. Join AX and BX.

Step 4: Draw perpendicular bisectors of AX and BX to intersect AB at Y and Z respectively. Join AB and AC.

Then, ABC is the required triangle.