1. Construct the right angled ΔPQR, where m∠Q = 90°, QR = 8cm and PR = 10 cm.
Solution:

Steps:
Step 1. Draw a line segment QR = 8 cm.
Step 2. Draw a ray QY, at point Q to make an angle of 90o i.e. ∠YQR = 90o.
Step 3. Now, R as a center with a radius of 10 cm, draw an arc that cuts the ray QY at P.
Step 4. Join PR.
Hence, ΔPQR is the required right-angled triangle.
2. Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.
Solution:
Let the ΔABC is a right-angled triangle at ∠B = 90o
Given,
AC is hypotenuse = 6 cm
BC = 4 cm
Now,
According to the question we have to construct the right-angled triangle.

Steps:
Step 1. Draw a line segment BC = 4 cm.
Step 2. Draw a ray BX, at point B to make an angle of 90o i.e. ∠XBC = 90o.
Step 3. Now, C as a center with a radius of 6 cm, draw an arc that cuts the ray BX at A.
Step 4. Join AC.
Hence, ΔABC is the required right-angled triangle.
3. Construct an isosceles right-angled triangle ABC, where m∠ACB = 90° and AC = 6 cm.
Solution:

Steps:
Step 1. Draw a line segment BC = 6 cm.
Step 2. Draw a ray CX, at point C to make an angle of 90o i.e. ∠XCB = 90o.
Step 3. Now, C as a center with a radius of 6 cm, draw an arc that cuts the ray CX at A.
Step 4. Join AB.
Hence, ΔABC is the required right-angled triangle.
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