Page 216 - Start Up Mathematics_7

5. Construct a ∆ ABC, whose rough sketch is shown in the given figure. D is a point in the
interior of ∆ ABC such that ∠ABD = 90° and ∠BAD = 40°. Using a ruler and protractor,
find the position of point D. Also find the A

(a) measure of length CD. 2.1 cm
(b) measure of ∠ADB.
(c) type of triangle ABC on the basis of its angles. B 6.4 cm C

Some NCERT Textbook Questions

1. Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a
point X, 4 cm away from l. Through X, draw a line m parallel to l.
2. Draw ∆PQR with PQ = 4 cm, QR = 3.5 cm and PR = 4 cm. What type of triangle is this?

3. Construct an isosceles triangle in which the lengths of each of its equal sides is 6.5 cm and
the angle between them is 110°.
4. Construct ∆ABC with BC = 7.5 cm, AC = 5 cm and m∠C = 60°.
5. Construct ∆PQR if PQ = 5 cm, m∠PQR = 105° and m∠QRP = 40°.
6. Examine whether you can construct ∆DEF such that EF = 7.2 cm, m∠E = 110° and
m∠F = 80°. Justify your answer.

7. Construct the right angled ∆PQR, where m∠Q = 90°, QR = 8 cm and PR = 10 cm.
8. Construct a right-angled triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm
long.

Exemplar Problems

1. A triangle can be constructed by taking its sides as:
(a) 1.8 cm, 2.6 cm, 4.4 cm (b) 2 cm, 3 cm, 4 cm
(c) 2.4 cm, 2.4 cm, 6.4 cm (d) 3.2 cm, 2.3 cm, 5.5 cm

2. A triangle can be constructed by taking two of its angles as:

(a) 110°, 40° (b) 70°, 115° (c) 135°, 45° (d) 90°, 90°
3. We can draw exactly one triangle whose angles are 70°, 30° and 80°. (True/False)

4. Construct a triangle PQR such that PQ = 6 cm, QR = 7 cm and PR = 4.5 cm.
5. Draw two parallel lines at a distance of 2.2 cm apart.

6. Construct an obtuse-angled triangle which has a base of 5.5 cm and base angles of 30° and
120°.
7. Construct an equilateral triangle ABC of side 6 cm.

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