NCERT Exemplar Solutions - Mathematics - class 7 solutions for Chapter 6 Triangles

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

(a) 6 (b) 5 (c) 3 (d) 4

Gayatri’s income ₹ 1,60,000 per year. She pays 15% of this as house rent and 10% of the remainder on her child’s education. The money left with her is

(a) ₹136000 (b) ₹120000 (c) ₹122400 (d) ₹14000

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

(a) They are equal angles

(b) They form a pair of adjacent angles

(c) They are complementary angles

(d) They are supplementary angles

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

(a) 35° (b) 45° (c) 55° (d) 70°

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

(a) obtuse (b) right (c) acute (d) straight

n 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?

(a) (i) only (b) (ii) only (c) (iii) only (d) (i) and(ii)

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?

(a) (i) only (b) (ii) only (c) (iii) only (d) (i) and (ii)

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

(a) Obtuse angled triangle (b) Acute-angled triangle

(c) Right-angled triangle (d) An Isosceles right triangle

5.2 is equal to

(a) 52% (b) 5.2% (c) 520% (d) 0.52%

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

(a) 85° (b) 90° (c) 25° (d) 35°

In ∆PQR,

(a) PQ – QR > PR

(b) PQ + QR < PR

(c) PQ – QR< PR

(d) PQ + PR< QR

In ∆ ABC,

(a) AB + BC > AC

(b) AB + BC < AC

(c) AB + AC < BC

(d) AC + BC < AB

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

(a) 25 m (b) 13 m (c) 18 m (d) 17 m

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

(a) an isosceles triangle only (b) a scalene triangle only

(c) an isosceles right triangle (d) scalene as well as a right triangle

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

(a) 3 m (b) 5 m (c) 4 m (d) 11 m

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

(a) Right-angled triangle (b) Acute angled triangle

(c) Obtuse angled triangle (d) Isosceles right-angled triangle

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

(a) Isosceles but not equilateral (b) Scalene

(c) Equilateral (d) Right-angled

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

(a) 120 cm (b) 122 cm (c) 71 cm (d) 142 cm

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

(a) 40° (b) 80° (c) 120° (d) 50°

Which of the following statements is not correct?

(a) The sum of any two sides of a triangle is greater than the third side

(b) A triangle can have all its angles acute

(c) A right-angled triangle cannot be equilateral

(d) Difference between any two sides of a triangle is greater than the third side

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

(a) 40° (b) 80° (c) 120° (d) 60°

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

(a) 1 cm and 10 cm

(b) 2 cm and 8 cm

(c) 3 cm and 16 cm

(d) 1 cm and 16 cm

From Fig. 6.10, the value of x is

(a) 75° (b) 90° (c) 120° (d) 60°

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

(a) 190° (b) 540° (c) 360° (d) 180°

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

(a) 55° (b) 40° (c) 50° (d) 45°

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

(a) 50° (b) 40° (c) 70° (d) 60°

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

(a) obtuse (b) acute (c) right (d) equilateral

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

(a) 55° (b) 65° (c) 50° (d) 60°

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

(a) 70° (b) 110° (c) 35° (d) 145°

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

(a) AD (b) BE (c) FC (d) DE

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

(a) 60° (b) 120° (c) 100° (d) 80°

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

(a) 67°, 51°, 62° (b) 70°, 83°, 27°

(c) 90°, 70°, 20° (d) 40°, 132°, 18°

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

(a) 4 cm (b) 3 cm (c) 5 cm (d) 32 cm

How many altitudes does a triangle have?

(a) 1 (b) 3 (c) 6 (d) 9

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

(a) Median (b) Angle bisector (c) Altitude (d) Hypotenuse

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

(a) 30°, 60° (b) 40°, 40°

(c) 70°, 70° (d) 70°, 60°

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

(a) 3 cm (b) 4 cm (c) 2 cm (d) 6 cm

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

(a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm

n a right-angled triangle ABC, if angle B = 90°, then which of the following is true? (a) AB2 = BC2 + AC2 (b) AC2 = AB2 + BC2

(c) AB = BC + AC (d) AC = AB + BC

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

In Fig. 6.16, if AB || CD, then,

(a) ∠ 2 = ∠ 3 (b) ∠ 1 = ∠ 4

(c) ∠ 4 = ∠ 1 + ∠ 2 (d) ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4

In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD⊥BC. Then, ∠B is equal to

(a) 80° (b) 20° (c) 40° (d) 30°

In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (Fig. 6.17). Measure of ∠ADC is

(a) 50° (b) 100° (c) 30° (d) 70°

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

(a) AC = DE (b) AB = EF (c) ∠A = ∠D (d) ∠C = ∠E

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

(a) ∠1 = ∠2 (b) ∠1 = ∠4 (c) ∠2 = ∠4 (d) ∠1 = ∠3

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

(a) 60° (b) 45° (c) 120s° (d) 90°

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

(a) RHS congruence criterion

(b) ASA congruence criterion

(c) SAS congruence criterion

(d) AAA congruence criterion

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

(a) RHS (b) ASA (c) SSS (d) SAS

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

(a) AAA (b) SSS (c) SAS (d) ASA

If ∆PQR is congruent to ∆STU (Fig. 6.20), then what is the length of TU?

(a) 5 cm (b) 6 cm (c) 7 cm (d) cannot be determined

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

(a) ∆ ABC ≅ ∆ DBC (b) ∆ ABC ≅ ∆CBD

(c) ∆ ABC ≅ ∆ DCB (d) ∆ ABC ≅ ∆BCD

The __________________ triangle always has altitude outside itself.

The sum of an exterior angle of a triangle and its adjacent angle is always ______________.

The longest side of a right-angled triangle is called its _____________

Median is also called _________in an equilateral triangle.

Measures of each of the angles of an equilateral triangle are ____________

In an isosceles triangle, two angles are always __________

In an isosceles triangle, angles opposite to equal sides are ___________________

If one angle of a triangle is equal to the sum of the other two, then the measure of that angle is ___________.

Every triangle has at least _________acute angle (s).

Two line segments are congruent, if they are of __________ lengths

Two angles are said to be ____________, if they have equal measures.

Two rectangles are congruent if they have same and ________________.

Two squares are congruent, if they have same ______________.

If ∆PQR and ∆XYZ are congruent under the correspondence QPR ↔ XYZ, then

(i) ∠R = ___________(ii) QR =_________ (iii) ∠P =_

(iv) QP = _____________ (v) ∠ Q = _______________ (vi) RP = ____________

In Fig. 6.22, ∆PQR ≅ ∆

In Fig. 6.23, ∆PQR ≅ ∆

In Fig. 6.24, ∆ ≅ ∆ PQR

In Fig. 6.25, ∆ ARO ≅ ∆

In Fig. 6.26, AB = AD and ∠BAC = ∠ DAC.

Then (i) ∆ ≅ ∆ ABC.

(ii) BC = _____.

(iii) ∠BCA = _________.

(iv) Line segment AC bisects and ______________.

In Fig. 6.27,

(i) ∠ TPQ = ∠ _____ + ∠ _____

(ii) ∠ UQR = ∠ _____ + ∠ _____

(iii) ∠ PRS = ∠ _____ + ∠ _____

In a triangle, the sum of squares of two sides is equal to the square of the third side.

The Sum of two sides of a triangle is greater than or equal to the third side.

The difference between the lengths of any two sides of a triangle is smaller than the length of the third side.

In ∆ABC, AB = 3.5 cm, AC = 5 cm, BC = 6 cm and in ∆PQR, PR= 3.5 cm, PQ = 5 cm, RQ = 6 cm. Then ∆ABC ≅ ∆PQR.

The Sum of any two angles of a triangle is always greater than the third angle.

The sum of the measures of three angles of a triangle is greater than 180°.

It is possible to have a right-angled equilateral triangle.

If M is the mid-point of a line segment AB, then we can say that AM and MB are congruent.

It is possible to have a triangle in which two of the angles are right angles.

It is possible to have a triangle in which two of the angles are obtuse.

It is possible to have a triangle in which two angles are acute.

Ncert exemplar solutions mathematics class 7 Solutions for Chapter 6 triangles