Assertion (A): In the figure, ∠BAC = 90° and AD ⊥ BC. The number of right triangles in the figure is 3.
Reason (R): If one angle of a triangle is 90°, then it is called a right angled triangle.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
Since AD ⊥ BC, both △ADB and △ADC have a right angle at D. Also, △BAC has a right angle at A. So there are three right triangles in the figure: △ADB, △ADC and △BAC. So, Assertion (A) is true.
Reason (R) states that a triangle with one 90° angle is a right angled triangle, which is true.
Each of △ADB, △ADC and △BAC is counted as a right triangle exactly because it has one angle of 90°. So, Reason (R) is the correct explanation of Assertion (A).
Hence, option 1 is the correct option.
Assertion (A): The point of intersection of the medians of a triangle is called its orthocentre.
Reason (R): There are three medians in a triangle.
Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Assertion (A) is true but Reason (R) is false.
Assertion (A) is false but Reason (R) is true.
Answer
The point of intersection of the medians of a triangle is called the centroid, not the orthocentre. (The orthocentre is the point of intersection of the altitudes.) So, Assertion (A) is false.
A triangle has three medians, one from each vertex to the mid-point of the opposite side. So, Reason (R) is true.
Hence, option 4 is the correct option.