Practical Geometry

24. 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

23. Choose the correct option in which a triangle cannot be constructed with the given lengths of sides.

• (A) 3 cm, 4 cm, 5 cm
• (B) 7 cm, 6 cm, 5 cm
• (C) 10 cm, 7 cm, 2 cm
• (D) 12 cm, 8 cm, 6 cm

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

• (A) 110°, 40°
• (B) 70°, 115°
• (C) 135°, 45°
• (D) 90°, 90°

21. In which of the following cases, a unique triangle can be drawn?

• (A) AB = 4 cm, BC = 8 cm and CA = 2 cm
• (B) BC = 5.2 cm, ∠B = 90° and ∠C = 110°
• (C) XY = 5 cm, ∠X = 45° and ∠Y = 60°
• (D) An isosceles triangle with the length of each equal side 6.2 cm

20. Suppose in ∆PQR, QR = 4.2 cm, ∠Q = 120° and PQ = 3.5 cm. If PM ⊥ QR, then which of the following is true?

• (A) PM lies to the right of PQ
• (B) PM lies to the left of PQ
• (C) PM lies inside to the ∆PQR
• (D) PM lies to the right of PQ and inside to the ∆PQR

19. Consider a line AB and take a point C outside it. We can draw a line parallel to AB using

• (A) Ruler only
• (B) Compass only
• (C) Ruler and compasses only
• (D) Ruler, divider and compasses only

18. Which among the following information is enough to construct a triangle?

• (A) The lengths of the sides is given
• (B) The perimeter of the triangle is given
• (C) The measures of three angles is given
• (D) The names of three vertices is given

17. In which of the following cases can a triangle be constructed?

• (A) Measures of three sides are given
• (B) Measures of two sides and the included angle are given
• (C) Measures of two angles and the included side are given
• (D) All the above

16. When an equilateral triangle PQR of sides 5.5 cm is constructed, which among the following is correct?

• (A) ∠P + ∠R = 110°
• (B) ∠P + ∠R > 110°
• (C) ∠P + ∠R = 120°
• (D) ∠P + ∠R < 110°

15. A sign board of shape like an isosceles triangle is made. If the unequal side is 7 cm and one of the equal sides is 6 cm. What is the measure of the third side?

• (A) 5 cm
• (B) 6 cm
• (C) 7 cm
• (D) > 7 cm

14. Construction of a right-angled triangle is based on

• (A) SSS criterion
• (B) SAS criterion
• (C) ASA criterion
• (D) RHS criterion

13. Adrija folds a sheet of paper. The dotted lines as shown in the figure are the creases formed, which are

named as l, m and n. Which among the following is true?

• (A) l ||n and l ⊥ m
• (B) l ||m and l ⊥ n
• (C) l ||n and l || m
• (D) l ⊥ n and l ⊥ m