Property of Median Drawn on Hypotenuse of the Right Triangle

Q.

Prove that the medians of an equilateral triangle are equal.

Q. The length of hypotenuse of a right angled triangle is 15. Find the length of median of its hypotenuse.

Q. Prove that the perimeter of the triangle is greater than the sum of its all medians

Q. A median is drawn on the hypotenuse of a right angled triangle. The length of the hypotenuse is 6 m . What is the length of the median ?

1. 6 m
2. 2 m
3. 3 m
4. 7 m

Q.

Prove that the median of an equilateral triangle are equal.

Q. Prove that Sum of all the three median is less than the perimeter of a triangle.

Q. Prove that the medians of an equilateral triangle are equal.

Q.

The perimeter of a triangle is.... the sum of its medians.

1. Less Than

2. Greater Than

3. Equal To

4. Greater Than Twice

Q. A median is drawn on the hypotenuse of a right angled triangle. The length of the hypotenuse is 14 m . What is the length of the median ?

1. 4 m
2. 16 m
3. 6 m
4. 7 m

Q. Assertion: If AD is a median of ∆ABC, then AB + AC > 2AD.
Reason: The angles opposite to equal sides of a triangle are equal.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. In triangle ABC, E is mid point of median AD and BE produced meets side AC at point Q. Show that BE : ESQ = 3:1.

Q. Match the following columns:

Column I	Column II
(a) In ∆ABC, if AB = AC and ∠A = 70°, then ∠C = ...... .	(p) less
(b) The vertical angle of an isosceles triangle is 120°. Each base angle is ...... .	(q) greater
(c) The sum of three medians of a triangle is ...... than the perimeter.	(r) 30°
(d) In a triangle, the sum of any two sides is always ...... than the third side.	(s) 55°

(a) ......,
(b) ......,
(c) ......,
(d) ......,

Q. A median is drawn on the hypotenuse of a right angled triangle. The length of the hypotenuse is 15 m. What is the length of the median ?

1. 7.5 m
2. 9 m
3. 15 m
4. 5 m

Q. A median is drawn on the hypotenuse of a right angled triangle. The length of the hypotenuse is 14 m . What is the length of the median ? [1 Mark]