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In figure, ∠BAC = 90°, AD ⊥ BC and ∠BAD = 50°, then ∠ACD is (a) 50° (b) 40° (c) 70° (d) 60°

The correct answer is (a) 50° Justification From the question, it is given that, ∠BAC = 90o AD ⊥ BC and ∠BAD = 50o So,... View Article

In figure PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is (a) 55⁰ (b) 40⁰ (c) 50⁰ (d) 45⁰

The correct answer is (b) 40o Justification Consider the ΔPQR. From the exterior angle property ∠RPU = ∠PRQ + ∠PQR... View Article

In figure the value of ∠A + ∠B + ∠C + ∠D + ∠E + ∠F is (a) 190⁰ (b) 540⁰ (c) 360⁰ (d) 180⁰

The correct answer is (c) 360o Justification From the figure, we can able to find out there are two triangles. So, consider the ΔABC,... View Article

From figure, the value of x is (a) 75⁰ (b) 90⁰ (c) 120⁰ (d) 60⁰

The correct answer is (c) 120o Justification We know that, exterior angle is equal to sum of opposite interior angles. From the... View Article

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

The correct answer is (c) 3 cm and 16 cm Justification From the given details we know that The length of the two sides of a triangle is 7 cm... View Article

In figure, BC = CA and ∠A = 40. Then, ∠ACD is equal to (a) 40⁰ (b) 80⁰ (c) 120⁰ (d) 60⁰

The correct answer is (b) 80o Justification We know that the exterior angle is equal to the sum of opposite interior angles. So, ∠ACD... View Article

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

The correct answer is (d) Difference of any two sides of a triangle is greater than the third side Justification The difference of the lengths... View Article

In ∆PQR, if PQ = QR and ∠Q = 100o, then ∠R is equal to (a) 40⁰ (b) 80⁰ (c) 120⁰ (d) 50⁰

The correct answer is (a) 40o Justification Given, In ∆PQR, PQ = QR so it is an isosceles triangle. Then, ∠P = ∠R So, let us assume... View Article

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

The correct answer is (d) 142 cm Justification Consider the rectangle PQRS, Given, length of rectangle PQ = 60 cm, Diagonal of the rectangle... View Article

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 correct answer is (c) Equilateral Justification In geometry, an equilateral triangle is a triangle that has all its sides... View Article

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

The correct answer is (c) Obtuse angled triangle Justification We know that sum of interior angles of a triangle is equal to 180o. Let... View Article

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

The correct answer is (b) 5 m Justification Consider PQ as the tree of height 7m and RS as the tree of height 4 m. So, consider the triangle... View Article

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

The correct answer is (b) a scalene triangle only Justification A scalene triangle is a triangle in which all three sides are in different... View Article

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 correct answer is (c) 18 m Justification From the given details we get to know that The top of a broken tree touches the ground at a... View Article

In ∆ ABC, (a) AB + BC > AC (b) AB + BC < AC (c) AB + AC < BC (d) AC + BC < AB

The correct answer is (a) AB + BC > AC Justification We know that from Triangle Inequality Theorem the sum of the lengths of any... View Article

In ∆PQR, (a) PQ – QR > PR (b) PQ + QR < PR (c) PQ – QR< PR (d) PQ + PR< QR

The correct answer is (c) PQ – QR< PR Justification The sum of the lengths of any two sides of a triangle is always greater than the... View Article

In figurePB = PD. The value of x is (a) 85⁰ (b) 90⁰ (c) 25⁰ (d) 35⁰

The correct answer is (c) 25o Justification Exterior angle of triangle is equal to sum of 2 opposite interior angles. As BC is straight line... View Article

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

The correct answer is (c) Right-angled triangle Justification In a right triangle, the three angles include one right angle and two acute... View Article

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)

The correct answer is (iii) only Justification In a right triangle, the three angles include one right angle and two acute angles since... View Article

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)

The correct answer is (d) (i) and(ii) Justification From the given details we know that One angle of an isosceles triangle is 70o. We know... View Article