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The area of △ ABC is 8 cm² in which AB = AC = 4 cm and ∠A = 90º. Write True or False and justify your answer.

The given statement is True Explanation Area of triangle = \(\begin{array}{l}\frac{1}{2}\end{array} \) × Base × Altitude Given that base= 4 cm... View Article

The area of a triangle with base 4 cm and height 6 cm is 24 cm². Write True or False and justify your answer.

The given statement is False Explanation Area of triangle = \(\begin{array}{l}\frac{1}{2}\end{array} \) × Base × Altitude Given that base= 4 cm... View Article

The area of an equilateral triangle with side 2√3 cm is (A) 5.196 cm² (B) 0.866 cm² (C) 3.496 cm² (D) 1.732 cm²

The correct answer is (A) 5.196 cm2 Equilateral Triangle An equilateral triangle has all three sides equal to each other.... View Article

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is (A) 1322 cm² (B) 1311 cm² (C) 1344 cm² (D) 1392 cm²

The correct answer is (C) 1344 cm2 Explanation We know that Area of triangle = √s(s-a)(s-b)(s-c) According to the given details... View Article

The perimeter of an equilateral triangle is 60 m. The area is (A) 10√3 m² (B) 15√3 m² (C) 20√3 m² (D) 100√3 m²

The correct answer is (D) 100√3 m2 Explanation We know that area of an equilateral triangle of side a =... View Article

An isosceles right triangle has area 8 cm². The length of its hypotenuse is (A) √32 cm (B) √16 cm (C) √48 cm (D) √24 cm

The correct answer is (A) √32 cm Explanation Let us assume height of triangle to be = h Given that the... View Article

Construct each of the following and give justification: A triangle PQR given that QR = 3cm, ∠ PQR = 45° and QP – PR = 2 cm.

Solution According to the given details We have to construct a triangle PQR such that QR = 3cm, ∠ PQR = 45°... View Article

Construct each of the following and give justification: A triangle if its perimeter is 10.4 cm and two angles are 45° and 120°.

Solution According to the given details We have to construct a triangle if its perimeter is 10.4 cm and two angles are... View Article

Construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8 cm. Bisect the smallest angle and measure each part.

Solution According to the given details We have to construct a triangle whose sides are 3.6 cm, 3.0 cm and 4.8... View Article

Draw an angle of 80° with the help of a protractor. Then construct angles of (i) 40° (ii)160° (iii) 120°.

Solution According to the given details We have to draw an angle of 80° with the help of a protractor. Then... View Article

Draw a line segment AB of 4 cm in length. Draw a line perpendicular to AB through A and B, respectively. Are these lines parallel?

Solution According to the given details A line segment AB of length 4cm. To draw a perpendicular to AB through A... View Article

Draw an angle of 110° with the help of a protractor and bisect it. Measure each angle.

Solution According to the given details An angle ABC = 110o and to draw the bisector of ∠ABC The steps of construction... View Article

A triangle ABC can be constructed in which AB = 5 cm, ∠A = 45° and BC + AC = 5 cm. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation We know that the Sum of any two sides of a triangle must be... View Article

An angle of 42.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is False Explanation We know that, 42.5° = 1/2 x 85° An angle of 85° cannot be constructed... View Article

An angle of 52.5° can be constructed. Write True or False in each of the following. Give reasons for your answer.

The given statement is True Explanation An angle of 52.5°can be constructed by bisecting angle 105° 52.5° = ½ ×... View Article

With the help of a ruler and a compass it is not possible to construct an angle of : (A) 37.5° (B) 40° (C) 22.5° (D) 67.5°

The correct answer is (B) 40° Solution With the help of a ruler and a compass, we can construct the angels,... View Article

Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle.

Given According to the given details Triangle ABC and l is the perpendicular bisector of BC. To Prove Angles bisector... View Article

ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.

Given ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and... View Article

If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.

Given According to the given details P, Q and R are the mid-points of the sides BC, CA and AB of... View Article

If non-parallel sides of a trapezium are equal, prove that it is cyclic.

Given According to the given details ABCD is a trapezium in which AD||BC Non-parallel sides AB and DC of the trapezium... View Article

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