Page 213 - Start Up Mathematics_7

6. Construct a ∆ ABC in which BC = 6.6 cm, AB = 5.2 cm and AC = 4.5 cm. Also draw a
perpendicular bisector of the side BC.
7. Construct an equilateral triangle whose each side measures 5.8 cm. Measure each of its
angles.
8. Construct a ∆ ABC in which AB = 5.5 cm, AC = 6.4 cm and ∠BAC = 45º.

9. Construct a ∆ PQR in which PQ = 5.2 cm, PR = 6.0 cm and ∠QPR = 55º.
10. Construct a ∆ ABC in which AB = 6.5 cm, AC = 4.9 cm and ∠BAC = 75º.
11. Construct a triangle ABC in which AB = 5.9 cm, ∠A = ∠B = 45º.
12. Construct a triangle ABC in which BC = 6.5 cm, ∠A = 45º and ∠B = 60º.

13. Construct a triangle ABC in which AB = 5.9 cm, BC = 5.9 cm and ∠B = 90º.
14. Construct a right-angled triangle whose one side is 4 cm and the hypotenuse is 5 cm.
15. Construct a right-angled triangle whose hypotenuse measures 6.5 cm and one of its acute
angle measures 60º. [Hint: First draw the hypotenuse and then its acute angles.]

At a Glance

1. A line can be drawn parallel to a given line, through a point not on it, either by constructing
equal alternate angles or by constructing equal corresponding angles.
2. Construction of a unique triangle is possible in the following cases:

(a) SSS criterion—three sides of a triangle are given.
(b) ASA criterion—two angles and an included side are given.

(c) SAS criterion—two sides and an included angle are given.
(d) RHS criterion—hypotenuse and a side of right triangle are given.
3. Since AAS—(angle, angle, side) can be converted to ASA, a triangle can be constructed.

4. SSA and AAA criterion are not sufficient to construct a unique triangle.

Review Exercises

Multiple ChoiCe Questions
1. The number of parallel lines that can be drawn from a point outside the line to it is:

(a) 0 (b) 1 (c) 2 (d) infinite
2. For lines l and m to be parallel, ∠a should be equal to:
2 1
(a) ∠1 (b) ∠2 l
(c) ∠3 (d) ∠4 a
3
3. A triangle which is impossible to construct has sides measuring: m
5 4
(a) 3 cm, 4 cm, 5 cm (b) 7 cm, 8 cm, 9 cm
(c) 4 cm, 6 cm, 10 cm (d) 10 cm, 18 cm, 12 cm

4. An angle that cannot be constructed using a ruler and compass only is:
(a) 15° (b) 22.5° (c) 37° (d) 60°

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