Medians

Q.

How many medians a triangle can have?

Q. In the given figure, AM is a median of $\Delta$ ABC.
Is AB + BC + CA > 2AM?

Q.

If AM is a median of triangle ABC, then which of the following relation will always hold good?

1. AB + BC + CA = 2AM

2. AB + BC + CA $>$​ 2AM

3. AB + BC + CA $<$​ 2AM

4. AB + BC + CA = AM

Q. In an equilateral triangle ABC, AD, BE and CF are the medians. If the length of AB = 7 cm, find the length of CE.

1. 3.5 cm
2. 3 cm
3. 6.5 cm
4. 7 cm

Q. Which of the following is/are true?

1. A median is line joining the vertex to the midpoint of any side.
2. A median always lies inside the triangle.
3. The point of intersection of medians is known as centroid.
4. A centroid always lies inside the triangle

Q. In the given figure, AM is a median of $\Delta$ ABC.
Is AB + BC + CA > 2AM?

Q. If G is the centroid of the $\Delta ABC$, then find the ratio of areas of $\Delta ADB$ to $\Delta ABC$.

1. 0.5
2. 0.25
3. 1
4. 2

Q. In an equilateral triangle ABC, AD, BE and CF are the medians. If the length of AB = 7 cm, find the length of CE.

1. 3 cm
2. 3.5 cm
3. 6.5 cm
4. 7 cm

Q. The point of intersection of medians is known as:

1. Incentre
2. Orthocentre
3. Centroid
4. Circumcentre

Q. All the medians and altitudes of a/an _______ triangle are same.

1. equilateral
2. scalene
3. right
4. isosceles

Q. In ∆PQR, D is the mid-point of side QR. Seg PD ⊥ seg QR. Then, can seg PD be the altitude as well as the median of ∆PQR? Give reasons for your answer.

Q.

Draw rough sketches for the following.
In $\Delta ABC,BE$ is a median.

Q. In a triangle, the line segment joining a vertex to the midpoint of the opposite side is called as .

1. altitude
2. median
3. angle bisector

Q. What is the ratio in which a median divides the opposite side?

1. 1 : 1
2. 2 : 1
3. 1 : 2
4. 1 : 3

Q. If $D$ is any point on the side $BC$ of $\Delta ABC$, then which of the inequality holds true?

1. $AB+BC+CA<2AD$
2. $AB+BC-CA>2AD$
3. $AB+BC+CA>2AD$
4. $AB+BC+AC=2AD$

Q. If $D$ is any point on the side $BC$ of $\Delta ABC$, then which of the inequality holds true?

1. $AB+BC+CA>2AD$
2. $AB+BC+CA<2AD$
3. $AB+BC-CA>2AD$
4. $AB+BC+AC=2AD$

Q. Draw any ∆XYZ and its three medians.

Q. In ∆UVW, UD is a median.


(1) Name the mid-point of seg VW.
(2) If l (VD) = 5 cm, then l (VW) = ?