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Construction of Triangle when its Hypotenuse and One Other Side are Given
(RHS Criterion)

Let us learn the construction of a right-angled triangle when its hypotenuse and one other side
are given, i.e., RHS criterion.
Study the following example.
Example 8: Construct a right DABC, right angled at B, in which
AC = 6 cm and AB = 4.5 cm.
Solution: Draw a rough sketch of DABC showing all measurements, this
will help us decide how to proceed.
Steps of construction: Rough Sketch
1. Draw a line segment AB = 4.5 cm and at B, draw BE ⊥ AB. E
2. With A as centre and radius = 6 cm, draw an arc to cut BE C
at C.
3. Join A to C. 6 cm
Thus, DABC is the required right-angled triangle. 90°

4.5 cm

Think and Answer
To construct an isosceles triangle, minimum how many sides are required?

Practice Time 15D

1. Construct a DJKL in which KL = 6.2 cm, JK = 5.5 cm and JL = 4.9 cm.
2. Construct a DABC in which AB = 4.8 cm, BC = 3.9 cm and CA = 4 cm.

3. Construct a triangle whose two sides are 3 cm and 4 cm, and the included angle is 70°.

4. Construct a DPQR in which PQ = 6 cm, QR = 4.5 cm, and ∠Q = 45°.
5. Construct a triangle whose two sides are 4.6 cm and 5.8 cm, and the included angle is 120°.
6. Construct a DPQR in which PQ = 3.8 cm, ∠P = 30°, and ∠Q = 45°.

7. Construct a DABC in which AB = 5.4 cm and ∠A = ∠B = 60°

8. Construct a triangle PQR whose two angles are ∠Q = 120° and ∠R = 30°, and the included side is
QR = 5.2 cm.

9. Construct a right-angled DABC whose hypotenuse measures 5.3 cm, and base BC measures 4.5 cm.
10. Construct a right-angled DPQR whose hypotenuse measures 6.5 cm, and ∠R = 60°.

Brain Sizzlers
Draw a line segment PQ = 6.4 cm. Take a point X in the middle of the line segment and construct an angle of
measure 165° using a ruler and compasses.

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