ANNUAL EXAM PYQS · CHAPTER 07

Triangles
CBSE Most Repeated PYQs

Solve official Class 9 Annual Examination Questions for Triangles. Click on options to test yourself, or click "Show Solution & Answer" for complete step-by-step working.

Q1Annual Exam 2024MCQ

1 Mark

Which of the following is NOT a criterion for congruence of triangles?

Q2Annual Exam 2023MCQ

1 Mark

In △ABC, AB = AC and ∠B = 50°, then ∠C is equal to:

Q3CBSE Pattern PYQMCQ

1 Mark

If △ABC ≅ △PQR, then which of the following is true?

Q4Annual Exam 2022MCQ

1 Mark

In △PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm, then length of PQ is:

Q5CBSE Model PYQAssertion-Reason

1 Mark

Assertion (A): Angles opposite to equal sides of an isosceles triangle are equal. Reason (R): Sides opposite to equal angles of a triangle are equal.

Q6Annual Exam 2021Assertion-Reason

1 Mark

Assertion (A): Two right triangles are congruent if hypotenuse and one side are equal. Reason (R): RHS criterion applies specifically to right-angled triangles.

Q7Annual Exam 2024Short Answer

2 Marks

In quadrilateral ACBD, AC = AD and AB bisects ∠A. Prove △ABC ≅ △ABD.

Q8Annual Exam 2023Short Answer

2 Marks

AD and BC are equal perpendiculars to line segment AB. Show CD bisects AB.

Q9CBSE Pattern PYQShort Answer

2 Marks

Line l is bisector of angle ∠A and B is any point on l. BP and BQ are perpendiculars. Show △APB ≅ △AQB.

Q10Annual Exam 2022Short Answer

2 Marks

In isosceles △ABC with AB = AC, D and E are points on BC such that BE = CD. Show AD = AE.

Q11CBSE Model PYQShort Answer

2 Marks

AB is a line segment and P is its midpoint. D and E are points such that ∠BAD = ∠ABE and ∠EPA = ∠DPB. Show △DAP ≅ △EBP.

Q12Annual Exam 2021Long Answer

3 Marks

In right triangle ABC right angled at C, M is midpoint of hypotenuse AB. C is joined to M and produced to D such that DM = CM. Show △AMC ≅ △BMD and ∠DBC = 90°.

Q13Annual Exam 2024Long Answer

3 Marks

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB. Prove altitudes are equal.

Q14Annual Exam 2023Long Answer

3 Marks

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show △ABE ≅ △ACF and AB = AC.

Q15CBSE Pattern PYQLong Answer

3 Marks

△ABC and △DBC are two isosceles triangles on same base BC. Show ∠ABD = ∠ACD.

Q16Annual Exam 2022Case Study

4 Marks

Case Study Scenario: A bridge structure forms two triangular frames △ABC and △PQR where AB = PQ, BC = QR and median AD = PM. Question: Prove that △ABC ≅ △PQR.

Q17CBSE Model PYQCase Study

4 Marks

Case Study Scenario: Two wooden ramps have equal hypotenuse length 13m and equal vertical height 5m. Question: Prove that the two ramps are congruent by RHS.

Q18Annual Exam PYQPYQ

5 Marks

Line segment AB is parallel to another line segment CD. O is midpoint of AD. Show △AOB ≅ △DOC and O is midpoint of BC.

Q19Annual Exam PYQPYQ

5 Marks

ABC is an isosceles triangle with AB = AC. Side BA is produced to D such that AD = AB. Show ∠BCD is a right angle.

Q20Annual Exam PYQPYQ

5 Marks

Triangles CBSE Most Repeated PYQs

Which of the following is NOT a criterion for congruence of triangles?

In △ABC, AB = AC and ∠B = 50°, then ∠C is equal to:

If △ABC ≅ △PQR, then which of the following is true?

In △PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm, then length of PQ is:

Assertion (A): Angles opposite to equal sides of an isosceles triangle are equal. Reason (R): Sides opposite to equal angles of a triangle are equal.

Assertion (A): Two right triangles are congruent if hypotenuse and one side are equal. Reason (R): RHS criterion applies specifically to right-angled triangles.

In quadrilateral ACBD, AC = AD and AB bisects ∠A. Prove △ABC ≅ △ABD.

AD and BC are equal perpendiculars to line segment AB. Show CD bisects AB.

Line l is bisector of angle ∠A and B is any point on l. BP and BQ are perpendiculars. Show △APB ≅ △AQB.

In isosceles △ABC with AB = AC, D and E are points on BC such that BE = CD. Show AD = AE.

AB is a line segment and P is its midpoint. D and E are points such that ∠BAD = ∠ABE and ∠EPA = ∠DPB. Show △DAP ≅ △EBP.

In right triangle ABC right angled at C, M is midpoint of hypotenuse AB. C is joined to M and produced to D such that DM = CM. Show △AMC ≅ △BMD and ∠DBC = 90°.

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB. Prove altitudes are equal.

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal. Show △ABE ≅ △ACF and AB = AC.

△ABC and △DBC are two isosceles triangles on same base BC. Show ∠ABD = ∠ACD.

Case Study Scenario: A bridge structure forms two triangular frames △ABC and △PQR where AB = PQ, BC = QR and median AD = PM. Question: Prove that △ABC ≅ △PQR.

Case Study Scenario: Two wooden ramps have equal hypotenuse length 13m and equal vertical height 5m. Question: Prove that the two ramps are congruent by RHS.

Line segment AB is parallel to another line segment CD. O is midpoint of AD. Show △AOB ≅ △DOC and O is midpoint of BC.

ABC is an isosceles triangle with AB = AC. Side BA is produced to D such that AD = AB. Show ∠BCD is a right angle.

In △ABC, AD is perpendicular bisector of BC. Show △ABC is isosceles in which AB = AC.

Triangles
CBSE Most Repeated PYQs