Two Triangles Having the Same Base & Equal Areas

Q. Question 1
The median of a triangle divides it into two:

A) Triangle of equal area
B) Congruent triangles
C) Right angle triangles
D) Isosceles triangle

Q.

Show that a median of a triangle divides it into two triangles of equal areas.

Q.

The base of a parallelogram is thrice its height. If the area is $867$ sq. cm, find the base of the parallelogram.

1. $34cm$

2. $51cm$

3. $17cm$

4. $68cm$

Q. XY is a line parallel to side BC of a triangle ABC. If BE||AC and CF||AB meet XY at E and F respectively,
show that $ar\left(\Delta ABE\right)=ar\left(\Delta ACF\right)$

Q. Question 7
D and E are points on sides AB and AC respectively of $\Delta ABC$ such that ar (DBC) = ar (EBC). Prove that DE || BC.

Q.

Given a triangle ABC and E is mid point of median AD of ∆ABC. If ar(∆BED) = 20 cm², then ar(∆ABC) is:

1. 10 cm²

2. 5 cm²

3. 60 cm²

4. 80 cm²

Q.

If the base of a parallelogram is 8 cm and its altitude is 5 cm, then its area is equal to

1. 15 cm²

2. 20 cm²

3. 40 cm²

4. 10 cm²

Q. Question 11 (v)
In $\Delta ABCand\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that AC = DF .

Q. The area of parallelogram of altitude 12cm is 108cm.square.Find the base of parallelogram

Q.

Area of a parallelogram is equal to

1. 

2. 

3. 

4. 

Q. Question 16
In the given figure, ar(DRC) = ar(DPC) and ar(BDP) = ar(ARC). Show that both the quadrilaterals ABCD and DCPR are trapeziums.

Q.

P is any point on the diagonals AC of a parallelogram ABCD.Prove that $ar\left(△ADP\right)=ar\left(△ABP\right)$.

Q. Question 6 (iii)
In the given figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that OB = OD. If AB = CD, then show that:
(iii) DA || CB or ABCD is a parallelogram.

Q.

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

Q.

In the figure, ABCD and AEFD are two parallelograms. Prove that
$\left(i\right)PE=FQ\left(ii\right)ar\left(△APE\right):ar\left(△PFA\right)=ar\left(△QFD\right):ar\left(△PFD\right)\left(iii\right)ar\left(△PEA\right)=ar\left(△QFD\right).$

Q. Question 15
Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar(AOD) = ar(BOC). Prove that ABCD is a trapezium.

Q. The median of a triangle divides it into two

(a) congruent triangle

(b) isosceles triangles

(c) right triangles

(d) triangles of equal areas

Q.

The adjacent sides of a parallelogram PQRS measure 34 cm and 20 cm and the diagonal QS measures 42 cm. Then, the area of parallelogram is:

1. 545 cm²

2. 924 cm²

3. 672 cm²

4. 850 cm²

Q.

A circular park of radius 20 m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.

Q. Show that a median of a triangle divides it into two triangles of equal area.

Q.

Diagonals AC and BD of a trapezium ABCD with AB ll DC intersect each other at O. If area (∆AOD)=37sq cm, then area (∆BOC)= ?

1. 45 sq cm

2. 55.5 sq cm

3. 74 sq cm

4. 37 sq cm

Q.

The area of a parallelogram whose base is 4 cm and the height is 5 cm is

1. 20 cm

2. 30 cm²

3. 30 cm

4. 20 cm²

Q. The median AA of the \bigtriangleup ABC meets the side BC of the medial triangle ABC in P and CP meets AB in Q .Show that in the triangle ABC, AB=3A

Q. Question 10
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar (AOD) = ar (BOC).

Q.

D is midpoint of side BC of $△ABC$ and E is the midpoint of BD.If O is the midpoint of AE, prove that $ar\left(△BOE\right)=\frac{1}{8}ar\left(△ABC\right)$

Q.

The medians of a triangle ABC is intersect at G. Then

1. $area\left(\Delta AGB\right)=\frac{3}{4}area\left(\Delta ABC\right)$

2. $area\left(\Delta AGB\right)=\frac{2}{3}area\left(\Delta ABC\right)$

3. $area\left(\Delta AGB\right)=\frac{1}{3}area\left(\Delta ABC\right)$

4. $area\left(\Delta AGB\right)=\frac{1}{2}area\left(\Delta ABC\right)$

Q. PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. If BE || AC and CF || AB meet PQ at E and F, respectively. If the base and altitude of ΔABC are 6 cm and 8 cm, respectively, then find the area of ΔACF.

1. 12 $c{m}^2$
2. 24 $c{m}^2$
3. 48 $c{m}^2$
4. 54 $c{m}^2$

Q.

The median of a triangle divided it into two

(a) triangles of equal area

(b) congruent traingles

(c) isosceles triangles

(d) right triangles

Q.

Which of the following is a false statement ?

(a) A median of a triangle divides it into two triangles of equal area.

(b) The diagonals of a ||gm divide it into four triangles of equal area.

(c) In a $△ABC$, if E is the midpoint of median AD then ar($△ABC$)=$\frac{1}{4}ar\left(△ABC\right)$.

(d) In a trap. ABCD, it is given that AB||DC and the diagonals AC and BD intersect at O.Then, ar$\left(△AOB\right)=ar\left(△COD\right)$.

Q. Question 1
The median of a triangle divides it into two:

A) Triangle of equal area
B) Congruent triangles
C) Right angle triangles
D) Isosceles triangle