Similar Triangles PYQs
Overview
This page provides comprehensive Class 10 Maths Similar Triangles PYQs | Triangles. Similar Triangles previous year questions for Class 10 Maths Triangles. Practice CBSE board PYQs with step-by-step solutions on SJMaths.
Concept-wise CBSE Class 10 Questions with Step-by-Step Solutions
Qq1
2024
00:00
If ΔABC ~ ΔPQR, ∠A = 32° and ∠R = 65°, then the measure of ∠B is:
Step 1: Since ΔABC ~ ΔPQR, corresponding angles are equal.
Step 2: So ∠C = ∠R = 65° and ∠A = 32°.
Step 3: Using angle sum property of a triangle:
$∠A + ∠B + ∠C = 180°$
$32° + ∠B + 65° = 180°$
$∠B = 180° - 97° = 83°$
Final Answer: 83° (Option c)
Qq2
2023
00:00
In two similar triangles, if one angle of the first triangle is 50°, then the corresponding angle of the second triangle is:
Step 1: In similar triangles, corresponding angles are equal.
Step 2: Therefore, the corresponding angle is also 50°.
Final Answer: 50° (Option b)
Qq3
2024
00:00
If the ratio of the corresponding sides of two similar triangles is 3 : 5, then the ratio of their areas is:
Step 1: Ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 2: Given ratio of sides = 3 : 5.
Step 3: Ratio of areas = $(3/5)^2 = 9/25$.
Final Answer: 9 : 25 (Option c)
Qq4
2023
00:00
In ΔABC ~ ΔPQR, if AB = 4 cm, PQ = 6 cm and QR = 9 cm, find the length of BC.
Step 1: Since triangles are similar, ratio of corresponding sides is equal.
$\frac{AB}{PQ} = \frac{BC}{QR}$
$\frac{4}{6} = \frac{BC}{9}$
$BC = \frac{4}{6} \times 9 = 6$
Final Answer: 6 cm (Option b)
Qq5
2022
00:00
Which of the following is the correct criterion for similarity of two triangles?
Step 1: Two triangles are similar if two of their corresponding angles are equal.
Step 2: This is called the AA similarity criterion.
Final Answer: AA (Option d)
Qq6
2021
00:00
In ΔABC, DE ∥ BC. The ratio of AD : DB is equal to:
Step 1: By Basic Proportionality Theorem, a line parallel to one side of a triangle divides the other two sides in the same ratio.
Step 2: Therefore, AD / DB = AE / EC.
Final Answer: AE : EC (Option a)
Qq7
2020
00:00
If the ratio of the areas of two similar triangles is 16 : 25, then the ratio of their corresponding sides is:
Step 1: Ratio of areas = square of ratio of corresponding sides.
Step 2: Let ratio of sides = x : y.
$\left(\frac{x}{y}\right)^2 = \frac{16}{25}$
$\frac{x}{y} = \frac{4}{5}$
Final Answer: 4 : 5 (Option a)
Qq8
2024
00:00
In two similar triangles, the ratio of the corresponding sides is 2 : 3. If the smaller side is 6 cm, find the corresponding larger side.
Step 1: Ratio of corresponding sides = 2 : 3.
Step 2: Let the larger side be $x$.
$\frac{6}{x} = \frac{2}{3}$
$x = \frac{6 \times 3}{2} = 9$
Final Answer: 9 cm (Option b)
Qq9
2023
00:00
State the AA similarity criterion for two triangles.
Step 1: If two angles of one triangle are equal to two corresponding angles of another triangle, then the two triangles are similar.
Step 2: This is known as the AA (Angle–Angle) similarity criterion.
Final Answer: Triangles are similar if two corresponding angles are equal (AA criterion).
Qq10
2023
00:00
In ΔABC, DE ∥ BC. If AD = 3 cm, DB = 2 cm and AE = x cm, EC = 4 cm, find x.
Step 1: By Basic Proportionality Theorem:
$\frac{AD}{DB} = \frac{AE}{EC}$
$\frac{3}{2} = \frac{x}{4}$
$x = \frac{3}{2} \times 4 = 6$
Final Answer: 6 cm (Option b)
Qq11
2022
00:00
Which of the following is a correct criterion for similarity of two triangles?
Step 1: In similarity, the correct criterion among the given options is SAS.
Step 2: If two sides are in the same ratio and the included angle is equal, then triangles are similar.
Final Answer: SAS (Option c)
Qq12
2021
00:00
The ratio of the areas of two similar triangles is 25 : 36. Find the ratio of their corresponding sides.
Step 1: Ratio of areas = square of ratio of sides.
$\left(\frac{a}{b}\right)^2 = \frac{25}{36}$
$\frac{a}{b} = \frac{5}{6}$
Final Answer: 5 : 6 (Option a)
Qq13
2020
00:00
Prove that two triangles are similar if their corresponding angles are equal.
Step 1: Given two triangles with two pairs of corresponding equal angles.
Step 2: By AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Final Answer: Triangles are similar by AA similarity criterion.
Qq14
2019
00:00
If ΔABC ~ ΔPQR and AB/PQ = 2/5, find the ratio of their perimeters.
Step 1: Ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides.
Step 2: Given AB/PQ = 2/5.
Step 3: Therefore, ratio of perimeters = 2 : 5.
Final Answer: 2 : 5 (Option a)
Qq15
2024
00:00
The ratio of the areas of two similar triangles is 49 : 64. Find the ratio of their corresponding sides.
Step 1: Ratio of areas of similar triangles = square of ratio of corresponding sides.
$\left(\frac{a}{b}\right)^2 = \frac{49}{64}$
Step 2: Taking square root:
$\frac{a}{b} = \frac{7}{8}$
Final Answer: 7 : 8 (Option a)
Qq16
2023
00:00
In ΔABC, DE ∥ BC. Prove that ΔADE ~ ΔABC.
Step 1: Since DE ∥ BC, corresponding angles are equal:
$∠ADE = ∠ABC \text{ and } ∠AED = ∠ACB$
Step 2: Also, ∠A is common to both triangles.
Step 3: Hence, by AA similarity criterion, ΔADE ~ ΔABC.
Final Answer: ΔADE ~ ΔABC (by AA similarity criterion)
Qq17
2022
00:00
State the SSS similarity criterion for two triangles.
Step 1: If in two triangles, the corresponding sides are in the same ratio, then the triangles are similar.
Step 2: This is known as the SSS similarity criterion.
Final Answer: Triangles are similar if their corresponding sides are proportional (SSS).
Qq18
2021
00:00
Find the ratio of the altitudes of two similar triangles whose corresponding sides are in the ratio 3 : 4.
Step 1: In similar triangles, the ratio of corresponding altitudes is equal to the ratio of corresponding sides.
Step 2: Given ratio of sides = 3 : 4.
Step 3: Therefore, ratio of altitudes = 3 : 4.
Final Answer: 3 : 4 (Option a)
Qq19
2020
00:00
Find the ratio of the medians of two similar triangles if the ratio of their corresponding sides is 5 : 7.
Step 1: In similar triangles, the ratio of corresponding medians is equal to the ratio of corresponding sides.
Step 2: Given ratio of sides = 5 : 7.
Step 3: Hence, ratio of medians = 5 : 7.
Final Answer: 5 : 7 (Option a)
Qq20
2019
00:00
In ΔABC ~ ΔPQR, the ratio of their corresponding sides is 2 : 3. If the perimeter of ΔABC is 18 cm, find the perimeter of ΔPQR.
Step 1: Ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides.
Step 2: Given ratio of sides = 2 : 3.
Step 3: Let perimeter of ΔPQR = x cm.
$\frac{18}{x} = \frac{2}{3}$
$x = \frac{18 \times 3}{2} = 27$
Final Answer: Perimeter of ΔPQR = 27 cm
Qq21
2018
00:00
Prove the converse of AA similarity criterion.
Step 1: Given two triangles with two pairs of corresponding equal angles.
Step 2: By the converse of AA criterion, if two corresponding angles are equal, then the triangles are similar.
Final Answer: Converse of AA similarity criterion is proved.
Qq22
2025
00:00
Assertion (A): In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Reason (R): If two triangles are similar, then their corresponding sides are proportional.
Step 1: In similar triangles, corresponding sides are proportional.
Step 2: Ratio of areas of similar triangles equals the square of the ratio of corresponding sides.
Step 3: Therefore, both Assertion and Reason are true and Reason explains Assertion.
Final Answer: Both A and R are true and R is the correct explanation of A. (Option a)
Qq23
2024
00:00
In the given figure, ΔABC ~ ΔPQR. If AB = 3 cm, BC = 4 cm and AC = 5 cm, find the sides of ΔPQR when the scale factor is 2.
Step 1: Given scale factor = 2.
Step 2: Corresponding sides of similar triangles are in the same ratio.
$PQ = 2 \times AB = 2 \times 3 = 6$
$QR = 2 \times BC = 2 \times 4 = 8$
$PR = 2 \times AC = 2 \times 5 = 10$
Final Answer: Sides of ΔPQR are 6 cm, 8 cm and 10 cm.
Qq24
2023
00:00
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 1: Let ΔABC ~ ΔPQR with AB/PQ = BC/QR = CA/PR = k.
Step 2: Areas of similar triangles are proportional to the squares of their corresponding sides.
$\frac{ar(ABC)}{ar(PQR)} = k^2$
Final Answer: Ratio of areas = square of ratio of corresponding sides.
Qq25
2022
00:00
The ratio of the corresponding sides of two similar triangles is 4 : 9. Find the ratio of their areas.
Step 1: Ratio of areas of similar triangles = square of ratio of corresponding sides.
$\left(\frac{4}{9}\right)^2 = \frac{16}{81}$
Final Answer: 16 : 81 (Option c)
Qq26
2021
00:00
If the perimeters of two similar triangles are in the ratio 5 : 7, find the ratio of their corresponding sides.
Step 1: In similar triangles, the ratio of perimeters equals the ratio of corresponding sides.
Step 2: Given ratio of perimeters = 5 : 7.
Step 3: Therefore, ratio of corresponding sides = 5 : 7.
Final Answer: 5 : 7 (Option a)
If ΔABC ~ ΔPQR, ∠A = 32° and ∠R = 65°, then the measure of ∠B is:
Step 1: Since ΔABC ~ ΔPQR, corresponding angles are equal.
Step 2: So ∠C = ∠R = 65° and ∠A = 32°.
Step 3: Using angle sum property of a triangle:
$∠A + ∠B + ∠C = 180°$
$32° + ∠B + 65° = 180°$
$∠B = 180° - 97° = 83°$
Final Answer: 83° (Option c)
Qq2
2023
00:00
In two similar triangles, if one angle of the first triangle is 50°, then the corresponding angle of the second triangle is:
Step 1: In similar triangles, corresponding angles are equal.
Step 2: Therefore, the corresponding angle is also 50°.
Final Answer: 50° (Option b)
Qq3
2024
00:00
If the ratio of the corresponding sides of two similar triangles is 3 : 5, then the ratio of their areas is:
Step 1: Ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 2: Given ratio of sides = 3 : 5.
Step 3: Ratio of areas = $(3/5)^2 = 9/25$.
Final Answer: 9 : 25 (Option c)
Qq4
2023
00:00
In ΔABC ~ ΔPQR, if AB = 4 cm, PQ = 6 cm and QR = 9 cm, find the length of BC.
Step 1: Since triangles are similar, ratio of corresponding sides is equal.
$\frac{AB}{PQ} = \frac{BC}{QR}$
$\frac{4}{6} = \frac{BC}{9}$
$BC = \frac{4}{6} \times 9 = 6$
Final Answer: 6 cm (Option b)
Qq5
2022
00:00
Which of the following is the correct criterion for similarity of two triangles?
Step 1: Two triangles are similar if two of their corresponding angles are equal.
Step 2: This is called the AA similarity criterion.
Final Answer: AA (Option d)
Qq6
2021
00:00
In ΔABC, DE ∥ BC. The ratio of AD : DB is equal to:
Step 1: By Basic Proportionality Theorem, a line parallel to one side of a triangle divides the other two sides in the same ratio.
Step 2: Therefore, AD / DB = AE / EC.
Final Answer: AE : EC (Option a)
Qq7
2020
00:00
If the ratio of the areas of two similar triangles is 16 : 25, then the ratio of their corresponding sides is:
Step 1: Ratio of areas = square of ratio of corresponding sides.
Step 2: Let ratio of sides = x : y.
$\left(\frac{x}{y}\right)^2 = \frac{16}{25}$
$\frac{x}{y} = \frac{4}{5}$
Final Answer: 4 : 5 (Option a)
Qq8
2024
00:00
In two similar triangles, the ratio of the corresponding sides is 2 : 3. If the smaller side is 6 cm, find the corresponding larger side.
Step 1: Ratio of corresponding sides = 2 : 3.
Step 2: Let the larger side be $x$.
$\frac{6}{x} = \frac{2}{3}$
$x = \frac{6 \times 3}{2} = 9$
Final Answer: 9 cm (Option b)
Qq9
2023
00:00
State the AA similarity criterion for two triangles.
Step 1: If two angles of one triangle are equal to two corresponding angles of another triangle, then the two triangles are similar.
Step 2: This is known as the AA (Angle–Angle) similarity criterion.
Final Answer: Triangles are similar if two corresponding angles are equal (AA criterion).
Qq10
2023
00:00
In ΔABC, DE ∥ BC. If AD = 3 cm, DB = 2 cm and AE = x cm, EC = 4 cm, find x.
Step 1: By Basic Proportionality Theorem:
$\frac{AD}{DB} = \frac{AE}{EC}$
$\frac{3}{2} = \frac{x}{4}$
$x = \frac{3}{2} \times 4 = 6$
Final Answer: 6 cm (Option b)
Qq11
2022
00:00
Which of the following is a correct criterion for similarity of two triangles?
Step 1: In similarity, the correct criterion among the given options is SAS.
Step 2: If two sides are in the same ratio and the included angle is equal, then triangles are similar.
Final Answer: SAS (Option c)
Qq12
2021
00:00
The ratio of the areas of two similar triangles is 25 : 36. Find the ratio of their corresponding sides.
Step 1: Ratio of areas = square of ratio of sides.
$\left(\frac{a}{b}\right)^2 = \frac{25}{36}$
$\frac{a}{b} = \frac{5}{6}$
Final Answer: 5 : 6 (Option a)
Qq13
2020
00:00
Prove that two triangles are similar if their corresponding angles are equal.
Step 1: Given two triangles with two pairs of corresponding equal angles.
Step 2: By AA similarity criterion, if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
Final Answer: Triangles are similar by AA similarity criterion.
Qq14
2019
00:00
If ΔABC ~ ΔPQR and AB/PQ = 2/5, find the ratio of their perimeters.
Step 1: Ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides.
Step 2: Given AB/PQ = 2/5.
Step 3: Therefore, ratio of perimeters = 2 : 5.
Final Answer: 2 : 5 (Option a)
Qq15
2024
00:00
The ratio of the areas of two similar triangles is 49 : 64. Find the ratio of their corresponding sides.
Step 1: Ratio of areas of similar triangles = square of ratio of corresponding sides.
$\left(\frac{a}{b}\right)^2 = \frac{49}{64}$
Step 2: Taking square root:
$\frac{a}{b} = \frac{7}{8}$
Final Answer: 7 : 8 (Option a)
Qq16
2023
00:00
In ΔABC, DE ∥ BC. Prove that ΔADE ~ ΔABC.
Step 1: Since DE ∥ BC, corresponding angles are equal:
$∠ADE = ∠ABC \text{ and } ∠AED = ∠ACB$
Step 2: Also, ∠A is common to both triangles.
Step 3: Hence, by AA similarity criterion, ΔADE ~ ΔABC.
Final Answer: ΔADE ~ ΔABC (by AA similarity criterion)
Qq17
2022
00:00
State the SSS similarity criterion for two triangles.
Step 1: If in two triangles, the corresponding sides are in the same ratio, then the triangles are similar.
Step 2: This is known as the SSS similarity criterion.
Final Answer: Triangles are similar if their corresponding sides are proportional (SSS).
Qq18
2021
00:00
Find the ratio of the altitudes of two similar triangles whose corresponding sides are in the ratio 3 : 4.
Step 1: In similar triangles, the ratio of corresponding altitudes is equal to the ratio of corresponding sides.
Step 2: Given ratio of sides = 3 : 4.
Step 3: Therefore, ratio of altitudes = 3 : 4.
Final Answer: 3 : 4 (Option a)
Qq19
2020
00:00
Find the ratio of the medians of two similar triangles if the ratio of their corresponding sides is 5 : 7.
Step 1: In similar triangles, the ratio of corresponding medians is equal to the ratio of corresponding sides.
Step 2: Given ratio of sides = 5 : 7.
Step 3: Hence, ratio of medians = 5 : 7.
Final Answer: 5 : 7 (Option a)
Qq20
2019
00:00
In ΔABC ~ ΔPQR, the ratio of their corresponding sides is 2 : 3. If the perimeter of ΔABC is 18 cm, find the perimeter of ΔPQR.
Step 1: Ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides.
Step 2: Given ratio of sides = 2 : 3.
Step 3: Let perimeter of ΔPQR = x cm.
$\frac{18}{x} = \frac{2}{3}$
$x = \frac{18 \times 3}{2} = 27$
Final Answer: Perimeter of ΔPQR = 27 cm
Qq21
2018
00:00
Prove the converse of AA similarity criterion.
Step 1: Given two triangles with two pairs of corresponding equal angles.
Step 2: By the converse of AA criterion, if two corresponding angles are equal, then the triangles are similar.
Final Answer: Converse of AA similarity criterion is proved.
Qq22
2025
00:00
Assertion (A): In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. Reason (R): If two triangles are similar, then their corresponding sides are proportional.
Step 1: In similar triangles, corresponding sides are proportional.
Step 2: Ratio of areas of similar triangles equals the square of the ratio of corresponding sides.
Step 3: Therefore, both Assertion and Reason are true and Reason explains Assertion.
Final Answer: Both A and R are true and R is the correct explanation of A. (Option a)
Qq23
2024
00:00
In the given figure, ΔABC ~ ΔPQR. If AB = 3 cm, BC = 4 cm and AC = 5 cm, find the sides of ΔPQR when the scale factor is 2.
Step 1: Given scale factor = 2.
Step 2: Corresponding sides of similar triangles are in the same ratio.
$PQ = 2 \times AB = 2 \times 3 = 6$
$QR = 2 \times BC = 2 \times 4 = 8$
$PR = 2 \times AC = 2 \times 5 = 10$
Final Answer: Sides of ΔPQR are 6 cm, 8 cm and 10 cm.
Qq24
2023
00:00
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
Step 1: Let ΔABC ~ ΔPQR with AB/PQ = BC/QR = CA/PR = k.
Step 2: Areas of similar triangles are proportional to the squares of their corresponding sides.
$\frac{ar(ABC)}{ar(PQR)} = k^2$
Final Answer: Ratio of areas = square of ratio of corresponding sides.
Qq25
2022
00:00
The ratio of the corresponding sides of two similar triangles is 4 : 9. Find the ratio of their areas.
Step 1: Ratio of areas of similar triangles = square of ratio of corresponding sides.
$\left(\frac{4}{9}\right)^2 = \frac{16}{81}$
Final Answer: 16 : 81 (Option c)
Qq26
2021
00:00
If the perimeters of two similar triangles are in the ratio 5 : 7, find the ratio of their corresponding sides.
Step 1: In similar triangles, the ratio of perimeters equals the ratio of corresponding sides.
Step 2: Given ratio of perimeters = 5 : 7.
Step 3: Therefore, ratio of corresponding sides = 5 : 7.
Final Answer: 5 : 7 (Option a)