Class 10 Maths Chapter 6 Assertion and Reason Questions - Triangles

Assertion (A): In an equilateral triangle of side 3√3 cm, then the length of the altitude is 4.5 cm.

Reason (R): If a ladder 10 cm long reaches a window 8 m above the ground, then the distance of the foot of the ladder from the base of the wall is 6 m.

Assertion : In the ΔABC , AB = 24 cm , BC = 10 cm and AC = 26 cm , then ΔABC is a right angle triangle.

Reason : If in two triangles, their corresponding angles are equal, then the triangles are similar.

Assertion : The length of the side of a square whose diagonal is 16 cm, is 8√2 cm

Reason : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Assertion (A): Corresponding sides of two similar triangles are in the ratio of 2 : 3. If the area of the smaller triangle is 48 cm², then the area of the larger triangle is 108 cm².

Reason (R): If D is a point on the side BC of a triangle ABC such that ∠ADC = ∠BAC, then CA² = CB × CD.

Assertion : ABC and DEF are two similar triangles such that BC = 4 cm , EF = 5 cm and area of ΔABC = 64 cm² , then area of ΔDEF = 100 cm².

Reason : The areas of two similar triangles are in the ratio of the squares of teh corresponding altitudes.

Assertion : The areas of two similar triangles ABC and PQR are in the ratio 9 :16. If BC = 4.5 cm, then the length of QR is 6 cm.

Reason : The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.

Assertion (A): If D is a point on side QR of ΔPQR such that PD ⊥ QR, then ΔPQD ~ ΔRPD.

Reason (R): In the figure given below, if ∠D = ∠C then ΔADE ~ ΔACB.

Assertion : ABC is an isosceles, right triangle, right angled at C . Then AB² = 3AC²

Reason : In an isosceles triangle ABC if AC = BC and AB² = 2AC² , then ∠C = 90°

Assertion : In ∆ABC , AB = 6√3, AC = 12 cm and BC = 6cm then ∠B = 90°.

Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Assertion (A): If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, then triangles will be similar.

Reason (R): If the ratio of the corresponding altitudes of two similar triangles is 3/5, then the

ratio of their areas is 6/5.

Assertion : Two similar triangle are always congruent.

Reason : If the areas of two similar triangles are equal then the triangles are congruent.

Assertion : ABC is an isosceles triangle right angled at C then AB² = 2AC².

Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Assertion : ΔABC is an isosceles triangle right angled of C , then AB² = 2AC².

Reason : In right ΔABC , right angled at B, AC² =AB² +BC².

Assertion : ABC is an isosceles triangle with AC = BC. If AB² = 2 AC², then ΔABC is a right triangle.

Reason : If in a triangle, square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

Assertion : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm² and ar(ΔDEF) = 49cm² then, AB : DE = 6 :7

Reason : If ΔABC ~ ΔDEF , then ar(ΔABC)/ar(ΔDEF) = AB²/DE² = BC²/EF² = AC²/DF²

Assertion : In the ∆ABC , AB = 24 cm, BC = 7 cm and AC = 25 cm, then ∆ABC is a right angle triangle.

Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Assertion : In ∆ABC , DE|| BC such that AD = (7x - 4)cm, AE = (5 - 2)cm, DB = (3 + 4) cm and EC = 3 cm than x equal to 5.

Reason : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distant point, than the other two sides are divided in the same ratio.

Assertion : If a line intersects sides AB and AC of a Δ ABC at D and E respectively and is parallel to BC, then AD/AB = AE/AC

Reason : If a line is parallel to one side of a triangle then it divides the other two sides in the same ratio.

Assertion : Assertion : If in a ∆ABC , a line DE || BC , intersects AB in D and AC in E , then AB/AD = AC/AE

Reason : If a line is drawn parallel to one side of a triangle intersecting the other two sides, then the other two sides are divided in the same ratio.

Assertion : ΔABC ~ ΔDEF such that ar(ΔABC) = 36cm² and ar(ΔDEF) = 49cm². Then, the ratio of their corresponding sides is 6 : 7

Reason : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.