Practical Geometry

12. In ΔXYZ, let x, y and z denote the three sides. Which of the following is incorrect?

• (A) x – y > z
• (B) x + z > y
• (C) x – y < z
• (D) x + y < z

11. ΔPQR is constructed such that PQ = 5 cm, PR = 5 cm and ∠RPQ = 50°. What type of triangle it is?

• (A) An isosceles triangle
• (B) An acute-angled triangle
• (C) An obtuse-angled triangle
• (D) A right-angled triangle

10. How many perpendicular lines can be drawn to a line from a point not on it?

• (A) 1
• (B) 2
• (C) 0
• (D) Infinite

9. A triangle PQR is constructed with QR = 4 cm, PQ = 3 cm and RP = 5 cm. Which of the given statement is false?

• (A) RP is the hypotenuse of ΔPQR
• (B) ΔPQR is an equilateral triangle
• (C) ΔPQR is a right-angled triangle
• (D) ∠Q = 90°

8. Which angle of ΔABC is right angled if AB = 8 cm, AC = 6 cm, and BC = 10 cm?

• (A) ∠C
• (B) ∠A
• (C) ∠B
• (D) None of these

7. A line p and a point X not on it are given. Which of the following is used to draw a line parallel to p through X?

• (A) Corresponding angles are equal
• (B) Alternate angles are equal
• (C) Angle sum property of triangles
• (D) Pythagoras’ theorem

6. Given AB = 3 cm, AC = 5 cm, and ∠B = 30°. ΔABC cannot be uniquely constructed, with AC as base. Why?

• (A) The included angle of the given sides is given
• (B) The other two angles are not given
• (C) The vertex B cannot be uniquely located
• (D) The vertex A coincides with the vertex C

5. In ΔRST, SR = 5 cm, and ∠SRT = 45° and ∠RST = 45°. Which criterion can be used to construct ΔRST?

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

4. To construct a triangle ABC in which AB = 6.5 cm and ∠A = 70° is not possible when sum of BC and AC is equal to

• (A) 6.5 cm
• (B) 6.2 cm
• (C) 5.6 cm
• (D) 6.9 cm

3. The construction of a triangle ABC in which AB = 7 cm, ∠A = 60° is not possible when sum of BC and AC is equal to

• (A) 8.5 cm
• (B) 7.6 cm
• (C) 6.9 cm
• (D) 7.1 cm

2. Area of a right-angled triangle is given. To construct the triangle, we must know

• (A) hypotenuse of the triangle
• (B) measure of the acute angles
• (C) base of the triangle
• (D) height of the triangle

1. Which of the following triangle is not possible to construct with RHS criterion?

• (A) ∠P = 90°, PR = 5 cm, PQ = 5 cm
• (B) ∠A = 30°, ∠B = 45°, AB = 4.5 cm
• (C) ∠P = 90°, QR = 5 cm, PR = 3 cm
• (D) None of these