Page 231 - ICSE Math 7
P. 231
EXERCISE
1. Draw a line AB and take a point P outside it. Draw another line CD parallel to AB, which passes
through point P.
2. Draw a line AB and take a point P that is 5 cm away from it. Draw another line CD parallel to
AB, which passes through point P.
3. Given a line l, draw another line m parallel to l at a distance of 4.6 cm from it.
4. Construct a triangle when all its sides are 3.8 cm.
5. Construct isosceles triangles with the following measurements.
(a) AB = 4.2 cm, BC = CA = 5.4 cm (b) MN = 8 cm, ∠M = ∠N = 75°
6. Construct an isosceles triangle when one of its equal sides is 4.9 cm and the vertical angle is 40°.
7. Construct a right-angled triangle when one of its sides is 6 cm and the hypotenuse is 7 cm.
8. Construct a right-angled triangle whose two sides forming the right angle are 2.8 cm and 4.5 cm.
9. Construct a triangle whose two angles are 30° and 90° and the included side is 5.6 cm.
10. Construct a triangle whose two angles are 50° each and the included side is 6 cm.
11. Construct an equilateral triangle with side 6 cm. Construct an incircle of this triangle.
12. Construct a triangle PQR with PQ = 6.7 cm, ∠RPQ = 60° and ∠PQR = 90°. Locate its circumcentre
and draw its circumcircle.
13. Construct the circumcircle of an isosceles triangle whose one of the equal sides is 3.5 cm and
the vertical angle is 84°.
14. Construct a right-angled triangle whose one side is 4.5 cm and the hypotenuse is 7 cm. Draw its
incentre.
AT A GLANCE
¾ 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.
¾ 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.
¾ Since AAS—(angle, angle, side) can be converted to ASA, a triangle can be constructed.
¾ SSA and AAA criterion are not sufficient to construct a unique triangle.
¾ A circle which passes through all the three vertices of a triangle is called the circumcircle of the
triangle.
¾ A circle drawn inside a triangle touching all the three sides of the triangle is known as the incircle
of the triangle.
217
