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In figure M is the mid-point of both AC and BD. Then (a) ∠1 = ∠2 (b) ∠1 = ∠4 (c) ∠2 = ∠4 (d) ∠1 = ∠3

The correct answer is (b) ∠1 = ∠4 Justification From the figure, we observe that M is the mid-point of both AC and BD. By the... View Article

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

The correct answer is (b) AB = EF Justification Given that ∆CAB ≅ ∆EDF ∴ AC = DE AB = DF BC = FE ∠A =∠D ∠C =... View Article

In ∆ABC, ∠Α = 50°, ∠B = 70° and bisector of ∠C meets AB in D (figure). Measure of ∠ADC is (a) 50° (b) 100° (c) 30° (d) 70°

The correct answer is (b) 100° Justification Let us consider the triangle ABC We know that, from the angle sum property of... View Article

In ∆ABC, ∠Α = 100°, AD bisects ∠A and AD⊥BC. Then, ∠B is equal to (a) 80⁰ (b) 20⁰ (c) 40⁰ (d) 30⁰

The correct answer is (c) 40o Justification Let us consider the triangle ABC, From the figure, we observe that AD bisects ∠Α... View Article

In figure, if AB || CD, then, (a) ∠ 2 = ∠ 3 (b) ∠ 1 = ∠ 4 (c) ∠ 4 = ∠ 1 + ∠ 2 (d) ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4

The correct answer is (d) ∠ 1 + ∠ 2 = ∠ 3 + ∠ 4 Justification From the property of the triangle, we know that The exterior... View Article

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

The correct answer is (d) has its altitude outside the triangle... View Article

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

The correct answer is (b) AC2 = AB2 + BC2 Justification (b) AC2 = AB2 + BC2 … From Pythagoras theorem, we know... View Article

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

The correct answer is (b) 4 cm Justification From Pythagoras theorem AC2 = AB2 + BC2 52 = AB2 + 32 AB2 = 25 –... View Article

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

The correct answer is (d) 6 cm Justification We know that, The sum of the lengths of any two sides of a triangle is always greater than the... View Article

The measures of ∠x and ∠y in figure are respectively (a) 30°, 60° (b) 40°, 40° (c) 70°, 70° (d) 70°, 60°

The correct answer is (d) 70°, 60° Justification We know that the exterior angle is the sum of the interior opposite angles of the... View Article

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 correct answer is (a) Median Justification A line segment that joins any vertex of the triangle and the mid-point of its opposite side is... View Article

How many altitudes does a triangle have? (a) 1 (b) 3 (c) 6 (d) 9

The correct answer is (b) 3 Justification We know that the altitude of a triangle is the perpendicular drawn from the vertex of the triangle to... View Article

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

The correct answer is (c) 5 cm Justification We know that, The sum of the lengths of any two sides of a triangle is always greater than the... View Article

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°

The correct answer is (d) 40°, 132°, 18° Justification We know that sum of angles of a triangle is equal to 180o. But, 40o +... View Article

In ∆PQR, if ∠ P = 60⁰, and ∠ Q = 40⁰, then the exterior angle formed by producing QR is equal to (a) 60⁰ (b) 120⁰ (c) 100⁰ (d) 80⁰

The correct answer is (c) 100o Justification As we know that, the exterior angle is the sum of opposite interior angles. Then, the exterior... View Article

In ∆ABC, 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

The correct answer is (b) BE Justification We know that the median of a triangle divides the opposite side into two equal parts. Hence, BE... View Article

If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is (a) 70⁰ (b) 110⁰ (c) 35⁰(d) 145⁰

The correct answer is (d) 145o Justification From the question, it is given that, one of the angles of a triangle is 110o We know that sum... View Article

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) 55o (b) 65o (c) 50o (d) 60o

The correct answer is (b) 65o Justification Let us assume the interior opposite angles are Q and Q. Then, 130o = Q + Q … [from... View Article

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

The correct answer is (c) right Justification A right triangle is the one in which the measure of any one of the interior angles is 90 degrees.... View Article

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

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