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

Solution:

We know that

We can draw a triangle if two angles and a side measurement are provided.

The construction of a triangle is according to the following criteria

A unique triangle can be drawn if

1. All 3 sides are provided

2. 2 sides and an included angle is provided

3. 2 angles and an included angle is provided

4. The measure of the side and a hypotenuse of a right triangle is provided

Therefore, a unique triangle can be drawn XY = 5 cm, ∠X = 45° and ∠Y = 60°.

✦ Try This: In which of the following cases, a unique triangle can be drawn

(a) AB = 5 cm, BC = 9 cm and CA = 3 cm

(b) BC = 6.2 cm, ∠B = 90° and ∠C = 120°

(c) XY = 6 cm, ∠X = 55° and ∠Y = 50°

(d) An isosceles triangle with the length of each equal side 7.2 cm.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 10

NCERT Exemplar Class 7 Maths Chapter 12 Problem 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

Summary:

A unique triangle can be drawn if XY = 5 cm, ∠X = 45° and ∠Y = 60°.

☛ Related Questions:

• Which of the following has a line of symmetry
• Which of the following are reflections of each other
• Which of these nets is a net of a cube