CBSE BOARD PYQS · CHAPTER 06

Triangles
CBSE Most Repeated PYQs

Solve official CBSE Previous Year Board Questions (2015-2024) for Triangles. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1CBSE 2024, 2020MCQ

1 Mark

In △ABC, DE || BC such that AD = 3 cm, DB = 5 cm, AE = 4.5 cm. Then EC is:

Q2CBSE 2023, 2019MCQ

1 Mark

If △ABC ~ △DEF and AB/DE = 1/3, then Area(△ABC) / Area(△DEF) is:

Q3CBSE 2022, 2018MCQ

1 Mark

Sides of two similar triangles are in ratio 4 : 9. Areas of these triangles are in ratio:

Q4CBSE 2024, 2021MCQ

1 Mark

A vertical pole of length 6 m casts shadow 4 m long on ground. At same time tower casts shadow 28 m long. Height of tower is:

Q5CBSE 2023, 2017Assertion-Reason

1 Mark

Assertion (A): If line divides any two sides of a triangle in same ratio, line is parallel to third side. Reason (R): This statement is known as Converse of Basic Proportionality Theorem.

Q6CBSE 2020, 2016Assertion-Reason

1 Mark

Assertion (A): All congruent triangles are similar. Reason (R): All similar triangles are congruent.

Q7CBSE 2024, 2020Short Answer

2 Marks

In △ABC, DE || BC. AD = x, DB = x-2, AE = x+2, EC = x-1. Find x.

Q8CBSE 2023, 2019Short Answer

2 Marks

Diagonals of trapezium ABCD with AB || DC intersect at O. Show AO/BO = CO/DO.

Q9CBSE 2022, 2018Short Answer

2 Marks

A ladder 10m long reaches window 8m above ground. Find distance of foot of ladder from wall.

Q10CBSE 2024, 2021Short Answer

2 Marks

In △ABC, AD ⊥ BC. Show that AB² + CD² = AC² + BD².

Q11CBSE 2023, 2017Short Answer

2 Marks

CM and RN are medians of △ABC and △PQR respectively. If △ABC ~ △PQR, show △AMC ~ △PNR.

Q12CBSE 2020, 2016Long Answer

3 Marks

State and prove Basic Proportionality Theorem (Thales Theorem).

Q13CBSE 2024, 2020Long Answer

3 Marks

BL and CM are medians of right triangle ABC right angled at A. Prove 4(BL² + CM²) = 5BC².

Q14CBSE 2023, 2019Long Answer

3 Marks

In equilateral triangle ABC, D is a point on BC such that BD = 1/3 BC. Prove 9AD² = 7AB².

Q15CBSE 2022, 2018Long Answer

3 Marks

In an isosceles triangle ABC with AC = BC, if AB² = 2AC², prove that △ABC is right angled.

Q16CBSE 2024, 2021Case Study

4 Marks

Case Study Scenario: A girl of height 90 cm is walking away from base of lamp-post at speed of 1.2 m/s. Lamp is 3.6 m above ground. Question: Find length of her shadow after 4 seconds.

Q17CBSE 2023, 2017Case Study

4 Marks

Case Study Scenario: Vijay is preparing for Board exams. He sets up triangular study frame ABC where DE || BC. Question: If AD = 2.4 cm, DB = 3.6 cm, AE = 3.2 cm, find AC.

Q18CBSE Official Board PYQPYQ

5 Marks

Prove that sum of squares of sides of a rhombus is equal to sum of squares of its diagonals.

Q19CBSE Official Board PYQPYQ

5 Marks

O is any point inside a rectangle ABCD. Prove OB² + OD² = OA² + OC².

Q20CBSE Official Board PYQPYQ

5 Marks

Triangles CBSE Most Repeated PYQs

In △ABC, DE || BC such that AD = 3 cm, DB = 5 cm, AE = 4.5 cm. Then EC is:

If △ABC ~ △DEF and AB/DE = 1/3, then Area(△ABC) / Area(△DEF) is:

Sides of two similar triangles are in ratio 4 : 9. Areas of these triangles are in ratio:

A vertical pole of length 6 m casts shadow 4 m long on ground. At same time tower casts shadow 28 m long. Height of tower is:

Assertion (A): If line divides any two sides of a triangle in same ratio, line is parallel to third side. Reason (R): This statement is known as Converse of Basic Proportionality Theorem.

Assertion (A): All congruent triangles are similar. Reason (R): All similar triangles are congruent.

In △ABC, DE || BC. AD = x, DB = x-2, AE = x+2, EC = x-1. Find x.

Diagonals of trapezium ABCD with AB || DC intersect at O. Show AO/BO = CO/DO.

A ladder 10m long reaches window 8m above ground. Find distance of foot of ladder from wall.

In △ABC, AD ⊥ BC. Show that AB² + CD² = AC² + BD².

CM and RN are medians of △ABC and △PQR respectively. If △ABC ~ △PQR, show △AMC ~ △PNR.

State and prove Basic Proportionality Theorem (Thales Theorem).

BL and CM are medians of right triangle ABC right angled at A. Prove 4(BL² + CM²) = 5BC².

In equilateral triangle ABC, D is a point on BC such that BD = 1/3 BC. Prove 9AD² = 7AB².

In an isosceles triangle ABC with AC = BC, if AB² = 2AC², prove that △ABC is right angled.

Case Study Scenario: A girl of height 90 cm is walking away from base of lamp-post at speed of 1.2 m/s. Lamp is 3.6 m above ground. Question: Find length of her shadow after 4 seconds.

Case Study Scenario: Vijay is preparing for Board exams. He sets up triangular study frame ABC where DE || BC. Question: If AD = 2.4 cm, DB = 3.6 cm, AE = 3.2 cm, find AC.

Prove that sum of squares of sides of a rhombus is equal to sum of squares of its diagonals.

O is any point inside a rectangle ABCD. Prove OB² + OD² = OA² + OC².

If △ABC ~ △PQR, AD & PM are medians of △ABC & △PQR respectively, prove AD/PM = AB/PQ.

Triangles
CBSE Most Repeated PYQs