Assertion and Reason Questions for Class 9 Maths Chapter 7 Triangles

Here we are providing assertion reason questions for class 9 maths. In this article, we are covering assertion reason questions for class 9 Maths Chapter 7 Triangles. Solutions are also provided. Students are suggested to solve the questions by themselves. After completing all questions, refer to answers and solutions for better understanding.

Assertion and Reason Questions for Class 9 Maths Chapter 7 Triangles

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(C) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Q.1. Assertion : In the adjoining figure, X and Y are respectively two points on equal sides AB and AC of ΔABC such that AX = AY then CX = BY.
Reason: If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent

Answer

Answer: (a)

Q.2. Assertion : In the given figure, BO and CO are the bisectors of ∠B and ∠C respectively. If ∠A = 50° then ∠BOC = 115°
Reason: The sum of all the interior angles of a triangle is 180⁰

Answer

Answer: (a)

Q.3. Assertion: Two angles measures a – 60° and 123º – 2a. If each one is opposite to equal sides of an isosceles triangle, then the value of a is 61°.
Reason: Sides opposite to equal angles of a triangle are equal.

Answer

Answer: (b)

Q.4. Assertion : In ΔABC, ∠C = ∠A, BC = 4 cm and AC = 5 cm. Then, AB = 4 cm
Reason: In a triangle, angles opposite to two equal sides are equal.

Answer

Answer: (b)

Q.5. Assertion : In ΔABC, BC = AB and B = 80°. Then, ∠A = 50°
Reason: In a triangle, angles opposite to two equal sides are equal

Answer

Answer: (a)

Q.6. Assertion : In ΔABC, D is the midpoint of BC. If DL I AB and DM I AC such that DL = DM, then BL = CM
Reason: If two angles and the included side of one triangle are equal to two angles

Answer

Answer: (b)

Q.7. Assertion : Angles opposite to equal sides of a triangle are not equal.
Reason : Sides opposite to equal angles of a triangle are equal.

Answer

Answer: (d)

Q.8. Assertion : In ΔABC, AB = AC and ∠B = 50°, then ∠C is 50°.
Reason: Angles opposite to equal sides of a triangle are equal.

Answer

Answer: (a)

Q.9. Assertion : ΔABC and ΔDBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at E, then ΔABD ≅ ΔACD
Reason: If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent.

Answer

Answer: (b)

Q.10. Assertion : In triangles ABC and PQR, ∠A = ∠P, ∠C = ∠R and AC = PR. The two triangles are congruent by ASA congruence.
Reason: If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent.

Answer

Answer: (a)

Q.11. Assertion : In ΔABC and ΔPQR, AB = PQ, AC = PR and ∠BAC = ∠QPR then ΔABC ≅ ΔPQR
Reason: Both the triangles are congruent by SSS congruence.

Answer

Answer: (c)

Q.12. Assertion: In the given figure, BE and CF are two equal altitudes of ΔABC then ΔABE ≅ ΔACF
Reason: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

Answer

Answer: (a)

Q.13. Assertion: In ABC, ∠A = ∠C and BC = 4 cm and AC = 3 cm then the length of side AB = 3 cm.
Reason: Sides opposite to equal angles of a triangle are equal.

Answer

Answer: (d)

Q.14. Assertion : If the altitudes from two vertices of a triangle to the opposite sides are equal, then the triangle is an isosceles triangle.
Reason: If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent.

Answer

Answer: (a)

Q.15. Assertion : In the given figure, ABCD is a quadrilateral in which AB || DC and P is the midpoint of BC. On producing, AP and DC meet at Q then DQ = DC + AB.
Reason: If two sides and the included angle of one triangle are equal to two sides

Answer

Answer: (b)

What are Assertion Reason Questions?

Certainly, Assertion Reason questions are a specific kind of questions often found in tests, especially in subjects like science and logic. In these questions, there are two statements: one is the Assertion (a statement) and the other is the Reason (an explanation). Your job is to see how these two statements relate to each other and decide if they are both correct or not.

Here’s a breakdown of the structure of an Assertion Reason question:

Assertion: The Assertion is a statement presented as a fact or claim. It may be true or false, and it is typically written in a straightforward manner.
Reason: The Reason is a statement that provides an explanation or justification for the Assertion. It can support or challenge the Assertion, depending on the accuracy of the Reasoning provided.
Options: Multiple options are typically provided alongside the Assertion Reason pair. The test-taker must choose the correct option that reflects the logical relationship between the Assertion and the Reason.

The possible options typically include:

a) If both the Assertion and the Reason are true, and the Reason is a correct explanation of the Assertion.

b) If both the Assertion and the Reason are true, but the Reason is not a correct explanation of the Assertion.

c) If the Assertion is true, but the Reason is false.

d) If the Assertion is false, but the Reason is true.

e) If both the Assertion and the Reason are false.

To answer Assertion Reason questions correctly, the test-taker needs to analyze the accuracy and logical connection between the two statements. It requires critical thinking, reasoning abilities, and a thorough understanding of the subject matter.

It is important to note that Assertion Reason questions can be challenging, as the test-taker needs to evaluate both statements independently and then determine the relationship between them. Careful reading, logical reasoning, and knowledge of the subject are essential for accurately answering such questions.

Preparation Tips to Score More in Assertion Reason Questions for Class 9 Maths

Assertion-reasoning questions can be daunting for CBSE students as they demand a deeper grasp and analytical thinking compared to regular multiple-choice queries. Such questions have two parts: an assertion and a reason. Students must decide if both are true and if the reason supports the assertion.

These questions go beyond rote knowledge, needing understanding of connections between facts. Fear might arise if students lack confidence in analyzing and judging the data. Also, their significant marks can intensify exam pressure.

However, with practice and a solid understanding of the concepts, students can overcome their fear of assertion-reasoning questions and perform well on their exams. It is important for students to read the questions carefully, understand the meaning of each statement, and analyze the relationship between the two statements before selecting their answer.

Preparing for assertion-reasoning questions can be challenging, but by adopting effective strategies, you can enhance your abilities and excel in exams. Here’s how you can prepare:

Understand the Concepts
Practice Regularly
Develop Analytical Skills
Take Notes
Seek Help

By following these strategies and putting in the effort to practice, you can improve your skills and perform well on assertion-reasoning questions.

Frequently Asked Questions (FAQs)

What is a triangle?

‘Tri’ means ‘three’
A closed figure formed by three intersecting lines is called a triangle. A triangle has three sides, three angles and three vertices.

What are the criteria for congruency?

(1) SAS congruence rule
(2) ASA congruence rule
(3) AAS congruence rule
(4) SSS congruence rule
(5) RHS congruence rule

What is SSS Criteria for Congruency?

If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

What is SAS Criteria for Congruency?

Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

What is ASA Criteria for Congruency?

Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.

What is AAS Criteria for Congruency?

Two triangles are said to be congruent to each other if two angles and one side of one triangle are equal to two angles and one side of the other triangle.

Why AAA and SSA congruency rules are not valid?

For same angles the two triangles can have sides of different length. So, AAA is not a valid test for congruency.
SSA is also not a valid test for congruency as the angle is not included between the pairs of equal sides.

What is RHS Criteria for Congruency?

If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

Assertion and Reason Questions for Class 9 Maths Chapter 7 Triangles

Frequently Asked Questions (FAQs)

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