NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 6: Triangles

Multiple Choice Questions

The sides of a triangle have lengths (in cm) 10, 6.5 and a, where a is a whole number. The minimum value that a can take is

Triangle DEF of Fig. 6.6 is a right triangle with ∠E = 90°. What type of angles are ∠D and ∠F?

In Fig. 6.7, PQ = PS. The value of x is

In a right-angled triangle, the angles other than the right angle are

In an isosceles triangle, one angle is 70°. The other two angles are of

(i) 55° and 55°

(ii) 70° and 40°

(iii) any measure

In the given option(s) which of the above statement(s) are true?

In a triangle, one angle is of 90°. Then

(i) The other two angles are of 45° each

(ii) In remaining two angles, one angle is 90° and other is 45°

(iii) Remaining two angles are complementary

In the given option(s) which is true?

Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is

In Fig. 6.8, PB = PD. The value of x is

In ΔPQR,

In ΔABC,

The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is

The triangle ABC formed by AB = 5 cm, BC = 8 cm, AC = 4 cm is

Two trees 7 m and 4 m high stand upright on a ground. If their bases are 4 m apart, then the distance between their tops is

If in an isosceles triangle, each of the base angles is 40°, then the triangle is

If two angles of a triangle are 60° each, then the triangle is

The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is

In ΔPQR, if PQ = QR and ∠Q = 100°, then ∠R is equal to

Which of the following statements is not correct?

In Fig. 6.9, BC = CA and ∠A = 40°. Then, ∠ACD is equal to

The length of two sides of a triangle are 7 cm and 9 cm. The length of the third side may lie between

From Fig. 6.10, the value of x is

In Fig. 6.11, the value of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F is

In Fig. 6.12, PQ = PR, RS = RQ and ST ∥ QR. If the exterior angle RPU is 140°, then the measure of angle TSR is

In Fig. 6.13, ∠BAC = 90°, AD ⟂ BC and ∠BAD = 50°, then ∠ACD is

If one angle of a triangle is equal to the sum of the other two angles, the triangle is

If the exterior angle of a triangle is 130° and its interior opposite angles are equal, then measure of each interior opposite angle is

If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is

In ΔABC, AD is the bisector of ∠A meeting BC at D, CF ⟂ AB and E is the mid-point of AC. Then median of the triangle is

In ΔPQR, if ∠P = 60°, and ∠Q = 40°, then the exterior angle formed by producing QR is equal to

Which of the following triplets cannot be the angles of a triangle?

Which of the following can be the length of the third side of a triangle whose two sides measure 18 cm and 14 cm?

How many altitudes does a triangle have?

If we join a vertex to a point on opposite side which divides that side in the ratio 1:1, then what is the special name of that line segment?

The measures of ∠x and ∠y in Fig. 6.14 are respectively

If length of two sides of a triangle are 6 cm and 10 cm, then the length of the third side can be

In a right-angled triangle ABC, if angle B = 90°, BC = 3 cm and AC = 5 cm, then the length of side AB is

In a right-angled triangle ABC, if angle B = 90°, then which of the following is true?

Which of the following figures will have its altitude outside the triangle?

In Fig. 6.16, if AB ∥ CD, then

In ΔABC, ∠A = 100°, AD bisects ∠A and AD ⟂ BC. Then, ∠B is equal to

In ΔABC, ∠A = 50°, ∠B = 70° and bisector of ∠C meets AB in D. Measure of ∠ADC is

If for ΔABC and ΔDEF, the correspondence CAB ↔ EDF gives a congruence, then which of the following is not true?

In Fig. 6.18, M is the mid-point of both AC and BD. Then

If D is the mid-point of the side BC in ΔABC where AB = AC, then ∠ADC is

Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the

By which congruency criterion, the two triangles in Fig. 6.19 are congruent?

By which of the following criterion two triangles cannot be proved congruent?

If ΔPQR is congruent to ΔSTU (Fig. 6.20), then what is the length of TU?

If ΔABC and ΔDBC are on the same base BC, AB = DC and AC = DB (Fig. 6.21), then which of the following gives a congruence relationship?