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Chapter 8

Triangles — Assertion-Reason Type Questions

Class - 9 RS Aggarwal Mathematics Solutions

Assertion Reasoning Questions

Question 1

Assertion (A): The orthocentre of a triangle may lie in the exterior of the triangle.

Reason (R): The point of intersection of the medians of a triangle is called its orthocentre.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Answer

The point of intersection of the altitudes of a triangle is called orthocentre.

∴ Reason (R) is false.

In case of an obtuse angled triangle, altitudes of a triangle intersects outside of the triangle.

∴ Assertion (A) is true.

Hence, option 1 is the correct option.

Question 2

Assertion (A): If three angles of a triangle are equal to the corresponding three angles of another triangle, then the triangles are congruent.

Reason (R): Two triangles are said to be congruent, if and only if, one of them can be made to superimpose on the other so as to cover exactly.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Answer

If three angles of a triangle are equal to the corresponding three angles of another triangle, then the triangles are similar not necessarily congruent.

∴ Assertion (A) is false.

Two triangles are said to be congruent, if both corresponding sides and angles to be equal i.e. once of triangle can be made to superimpose on other.

∴ Reason (R) is true.

Hence, option 2 is the correct option.

Question 3

Sum of two sides of a triangle is greater than the third side. R.S. Aggarwal Mathematics Solutions ICSE Class 9.

Assertion (A): In △ABC, D is a point on side BC. AB + BC + AC > 2AD

Reason (R): Sum of two sides of a triangle is greater than the third side.

  1. A is true, R is false

  2. A is false, R is true

  3. Both A and R are true

  4. Both A and R are false

Answer

We know that,

Sum of two sides of a triangle is greater than the third side is fundamental property of triangle.

∴ Reason (R) is true.

In △ABD,

⇒ AB + BD > AD ...(1) [Sum of any two sides of triangle is greater than the third side]

In △ADC,

⇒ AC + CD > AD ...(2) [Sum of any two sides of triangle is greater than the third side]

Adding eq.(1) and (2), we have:

⇒ AB + BD + AC + CD > AD + AD

⇒ AB + AC + BD + CD > 2AD

⇒ AB + AC + BC > 2AD

∴ Assertion (A) is true.

Hence, option 3 is the correct option.

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