Mathematics

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.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false

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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.

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Case Study
Ms Anu Gupta teaches mathematics to class 9 in a school. One day she drew a figure on the board in the class. She provided the following clues to the students.
AB || CD
O is the mid-points of AD
Based on this information, answer the following questions:
△OAB ≅ △ODC by which of the following congruent condition?
(a) SAS
(b) ASA
(c) SSS
(d) RHS
∠AOB = ∠DOC holds because:
(a) Alternate angles are equal
(b) Corresponding angles are equal
(c) Vertically opposite angles are equal
(d) None of these
Which of the following is correct?
(a) ∠A = ∠C
(b) ∠B = ∠D
(c) ∠B = ∠C
(d) ∠AOB = ∠OCB
Which of the following is correct?
(a) AO = OB
(b) AB = OB
(c) OD = CD
(d) OC = OB
Which of the following is not a congruent condition?
(a) ASA
(b) SSS
(c) AAA
(d) AAS
View Answer
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.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
View Answer
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.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false
View Answer