Theorem 3: Triangle (Altitude)

Q.

D is the mid-point of side BC of $\Delta ABC$ and E is the mid point of BD. If O is the midpoint of AE, then area of ($\Delta BOE$) is equal to

1. $\frac{1}{8}$ Area ($\Delta$ ABC)

2. $\frac{1}{6}$ Area ($\Delta$ ABC)

3. $\frac{1}{4}$ Area ($\Delta$ ABC)

4. $\frac{1}{3}$ Area ($\Delta$ ABC)

Q. If triangles ABC and DCB are such that $ar\left(△ABC\right)=ar\left(△DCB\right)$ as shown below, then AM= ____.

1. DN
2. ON
3. OD
4. None of the above

Q. In a triangle $ABC,E$ is the mid point of median $AD$. Using vectors show that $ar\left(BED\right)=\frac{1}{4}ar\left(ABC\right)$

Q. If the perimeter of an equilateral triangle is 12 cm then the length of each median is

1. $2\sqrt{5}$ cm
2. $\sqrt{3}$ cm
3. $2\sqrt{3}$ cm
4. $3\sqrt{2}$ cm

Q. Triangles ABC and DCB are such that $ar\left(△ABC\right)=ar\left(△DCB\right)$, where A and D lie on the opposite sides of BC. Which of the following options are correct?

1. $△AMO\cong △DNO$
2. BC bisects AD
3. $AO=\frac{1}{2}AD$
4. None of the above.

Q. In a triangle $ABC$, $E$ is the mid- point of median $AD$. Show that $ar\left(△BED\right)=\frac{1}{4}ar\left(△ABC\right)$.

Q.

Median divides a triangle into the triangle of unequal area

1. False

2. True

Q.

What is the area of $△ABC$ (in square cm) if AD is the median and area $△ADB$= 18 square cm?

__

Q.

If two triangles have equal area and stand on the same base, then the altitudes of the triangle are equal.

1. True

2. False

Q.

AD is median of triangle ABC and DE is median of triangle ABD. The ratio of area triangle BED : area triangle ABC

1. 1 : 2

2. 1 : 3

3. 1 : 4

4. 1 : 8

Q.

AD is the median of triangle ABC. The ratio of area of ABD : area of ACD is _______.

1. 2 : 1

2. 1 : 2

3. 1 : 3

4. 1 : 1

Q.

Median divides a triangle into the triangles of equal area.

1. False

2. True

Q. In $△ABC$, it is given that D is the midpoint of BC; E is the midpoint of BD and O is the midpoint of AE. Then, ar($△BOE$)=?