NCERT Exemplar Class 10 Maths - Chapter 6 Triangles

1. In Fig. 6.2, \(\angle BAC = 90^\circ\) and \(AD \perp BC\). Then,

(A) \( BD \cdot CD = BC^{2} \)
(B) \( AB \cdot AC = BC^{2} \)
(C) \( BD \cdot CD = AD^{2} \)
(D) \( AB \cdot AC = AD^{2} \)

Note: Refer to Fig. 6.2 in the original book (right triangle with altitude to hypotenuse).

Correct Answer: (C)

2. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Then, the length of the side of the rhombus is

(A) 9 cm (B) 10 cm (C) 8 cm (D) 20 cm

Correct Answer: (B)

3. If \(\triangle ABC \sim \triangle EDF\) and \(\triangle ABC\) is not similar to \(\triangle DEF\), then which of the following is not true?

(A) \( BC \cdot EF = AC \cdot FD \)
(B) \( AB \cdot EF = AC \cdot DE \)
(C) \( BC \cdot DE = AB \cdot EF \)
(D) \( BC \cdot DE = AB \cdot FD \)

Correct Answer: (C)

4. If in two triangles ABC and PQR, \(\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}\), then

(A) \(\triangle PQR \sim \triangle CAB\)
(B) \(\triangle PQR \sim \triangle ABC\)
(C) \(\triangle CBA \sim \triangle PQR\)
(D) \(\triangle BCA \sim \triangle PQR\)

Correct Answer: (A)

5. In Fig. 6.3, two line segments AC and BD intersect each other at the point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, \(\angle APB = 50^\circ\) and \(\angle CDP = 30^\circ\). Then, \(\angle PBA\) is equal to

(A) \(50^\circ\) (B) \(30^\circ\) (C) \(60^\circ\) (D) \(100^\circ\)

Note: Refer to Fig. 6.3 in the original book.

Correct Answer: (D)

6. If in two triangles DEF and PQR, \(\angle D = \angle Q\) and \(\angle R = \angle E\), then which of the following is not true?

(A) \(\dfrac{EF}{PR} = \dfrac{DF}{PQ}\)
(B) \(\dfrac{DE}{PQ} = \dfrac{EF}{RP}\)
(C) \(\dfrac{DE}{QR} = \dfrac{DF}{PQ}\)
(D) \(\dfrac{EF}{RP} = \dfrac{DE}{QR}\)

Correct Answer: (B)

7. In triangles ABC and DEF, \(\angle B = \angle E\), \(\angle F = \angle C\) and \(AB = 3 DE\). Then, the two triangles are

(A) congruent but not similar
(B) similar but not congruent
(C) neither congruent nor similar
(D) congruent as well as similar

Correct Answer: (B)

8. It is given that \(\triangle ABC \sim \triangle PQR\), with \(\dfrac{BC}{QR} = \dfrac{1}{3}\). Then, \(\dfrac{\mathrm{ar}(PRQ)}{\mathrm{ar}(BCA)}\) is equal to

(A) 9 (B) 3 (C) \(\dfrac{1}{3}\) (D) \(\dfrac{1}{9}\)

Correct Answer: (A)

9. It is given that \(\triangle ABC \sim \triangle DFE\), \(\angle A = 30^\circ\), \(\angle C = 50^\circ\), AB = 5 cm, AC = 8 cm and DF = 7.5 cm. Then, the following is true:

(A) DE = 12 cm, \(\angle F = 50^\circ\)
(B) DE = 12 cm, \(\angle F = 100^\circ\)
(C) EF = 12 cm, \(\angle D = 100^\circ\)
(D) EF = 12 cm, \(\angle D = 30^\circ\)

Correct Answer: (B)

10. If in triangles ABC and DEF, \(\dfrac{AB}{DE} = \dfrac{BC}{FD}\), then they will be similar, when

(A) \(\angle B = \angle E\)
(B) \(\angle A = \angle D\)
(C) \(\angle B = \angle D\)
(D) \(\angle A = \angle F\)

Correct Answer: (C)

11. If \(\triangle ABC \sim \triangle QRP\), \(\dfrac{\mathrm{ar}(ABC)}{\mathrm{ar}(PQR)} = \dfrac{9}{4}\), AB = 18 cm and BC = 15 cm, then PR is equal to

(A) 10 cm (B) 12 cm (C) \(\dfrac{20}{3}\) cm (D) 8 cm

Correct Answer: (A)

12. If S is a point on side PQ of a \(\triangle PQR\) such that PS = QS = RS, then

(A) \( PR \cdot QR = RS^{2} \)
(B) \( QS^{2} + RS^{2} = QR^{2} \)
(C) \( PR^{2} + QR^{2} = PQ^{2} \)
(D) \( PS^{2} + RS^{2} = PR^{2} \)

Correct Answer: (C)

Answers taken from the official NCERT Exemplar answer key. Figures are referenced from the original book.

NCERT Exemplar Problems – Class 10 Mathematics

Chapter 6: Triangles