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
(a) 6
(b) 5
(c) 3
(d) 4
Triangle DEF of Fig. 6.6 is a right triangle with ∠E = 90°. What type 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
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?
(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
In Fig. 6.8, PB = PD. The value of x is

(a) 85°
(b) 90°
(c) 25°
(d) 35°
In ΔPQR,
(a) PQ – QR > PR
(b) PQ + QR < PR
(c) PQ – QR < PR
(d) PQ + PR < QR
In ΔABC,
(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 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 ΔPQR, 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 of 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 two sides of a triangle are 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 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 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
(a) AD
(b) BE
(c) FC
(d) DE
In ΔPQR, 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 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
In 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?

(a)
(b)
(c)
(d)
In Fig. 6.16, if AB ∥ CD, then

(a) ∠2 = ∠3
(b) ∠1 = ∠4
(c) ∠4 = ∠1 + ∠2
(d) ∠1 + ∠2 = ∠3 + ∠4
In ΔABC, ∠A = 100°, AD bisects ∠A and AD ⟂ BC. Then, ∠B is equal to
(a) 80°
(b) 20°
(c) 40°
(d) 30°
In ΔABC, ∠A = 50°, ∠B = 70° and bisector of ∠C meets AB in D. Measure of ∠ADC is

(a) 50°
(b) 100°
(c) 30°
(d) 70°
If for ΔABC and ΔDEF, 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 ΔABC where AB = AC, then ∠ADC is
(a) 60°
(b) 45°
(c) 120°
(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 ΔPQR is congruent to ΔSTU (Fig. 6.20), then what is the length of TU?

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

(a) ΔABC ≅ ΔDBC
(b) ΔABC ≅ ΔCBD
(c) ΔABC ≅ ΔDCB
(d) ΔABC ≅ ΔABCD