**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 **Δ**ABC 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

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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 180^{0}

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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.

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Answer: (b)**Q.4. Assertion :** In **Δ**ABC, ∠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.

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Answer: (b)**Q.5. Assertion :** In **Δ**ABC, BC = AB and B = 80°. Then, ∠A = 50°**Reason:** In a triangle, angles opposite to two equal sides are equal

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Answer: (a)**Q.6. Assertion :** In **Δ**ABC, 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

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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.

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Answer: (d)**Q.8. Assertion : **In **Δ**ABC, AB = AC and ∠B = 50°, then ∠C is 50°.**Reason: **Angles opposite to equal sides of a triangle are equal.

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Answer: (a)**Q.9. Assertion :** **Δ**ABC and **Δ**DBC 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 **Δ**ABD **≅** **Δ**ACD**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.

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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.

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Answer: (a)**Q.11. Assertion : **In **Δ**ABC and **Δ**PQR, AB = PQ, AC = PR and ∠BAC = ∠QPR then **Δ**ABC **≅** **Δ**PQR**Reason: **Both the triangles are congruent by SSS congruence.

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Answer: (c)**Q.12. Assertion: **In the given figure, BE and CF are two equal altitudes of **Δ**ABC then **Δ**ABE **≅** **Δ**ACF**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.

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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.

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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.

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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

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Answer: (b)**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.

**How to express congruency?**

congruency can be expressed by the symbol **≅**