Figures on the Same Base and Between the Same Parallels

Q.

If two figures have same area, they must be congruent.

1. True

2. False

Q.

If two parallelograms have the same (or equal) bases and are between the same parallel lines, their areas will be equal.

1. 1:4

2. 1:3

Q.
Area of parallelogram ABCD equals to 100 $c{m}^2$. What is the area of $\Delta$ DEC?

1. $50c{m}^2$
2. $20c{m}^2$
3. $100c{m}^2$
4. $30c{m}^2$

Q. In the given Figure, $\square$ABCD is a trapezium. AB || DC .Points P and Q are midpoints of seg AD and seg BC respectively.
Then prove that, PQ || AB and PQ = $\frac{1}{2}$( AB + DC ).

Q. In the given figure, ABCD is a parallelogram then ar($\Delta AFB$) is

1. $8c{m}^2$
2. $\frac{11}{8}c{m}^2$
3. $5c{m}^2$
4. $\frac{6}{7}c{m}^2$

Q.

$l$ and $m$ are two parallel lines intersected by another pair of parallel lines $p$ and $q$ (see the given figure). Show that $△ABC\cong △CDA$.

Q. In the adjacent figure, $\square$ABCD is a trapezium AB || DC . Points M and N are midpoints of diagonal AC and DB respectively then prove that MN || AB .

Q. Question 11 (ii)
In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:

(ii) ar(AEDF) = ar(ABCDE)

Q.

Which of the following figures lie on the same base and between the same parallels.In such a case, write the common base and the two parallels.

Q.

Ram has a plot of land of the shape of a quadrilateral. Government wants to take some portion of his land to build a hospital. Ram agrees with the condition that he should be given equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented. [4 MARKS]

Q.

In the figure, ABCD is a parallelogram, AB and BC are equal to 15 cm and 6 cm respectively. If DF = 4 cm, what is the value of BE?

1. 6 cm
2. 8 cm
3. 10 cm
4. 12 cm

Q.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that

(i) ΔDAP ≅ ΔEBP

(ii) AD = BE

Q.

Observe the given figure and choose the correct statement

1. AB ║ AD

2. AB ║ CD

3. BC║ DC

4. AD ║ CD

Q. Which of the following figures lie on the same base and between the same parallel lines?

1. 

2. 

3. 

4. 

Q.

In a trapezium ABCD, AB||DC and M is the midpoint of BC.Through M, a line PQ||AD has been drawn which meets AB in P and DC produced in Q, as shown in the adjoining figure. Prove that ar(ABCD)=ar(APQD).

Q. Question 1 (vi)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q. Question 1 (i)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q. ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that ar (Δ POA) = ar (Δ QOC).

Q. Question 1 (iii)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q.

In given figure, ABCDE is any pentagon.BP is drawn parallel to AC and meets DC produced at P. EQ is drawn parallel to AD and meets CD produced at Q. Then, which of the following statements is true?

1. $Area\left(ABCDE\right)=2Area\left(\Delta ADQ\right)$

2. $Noneofthese$

3. $Area\left(ABCDE\right)=Area\left(\Delta ACQ\right)$

4. $Area\left(ABCDE\right)=Area\left(\Delta APQ\right)$

Q. Question 1 (i)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q. Question 14
In the given figure, AP || BQ || CR. Prove that ar(AQC) = ar(PBR).

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. Question 1 (iii)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q. Question 1 (iv)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q.

Out of the following given figures, which are on the same base but not between the same parallels?

Q. In Fig. 8, ABCD is a trapezium in which AB || DC. BD is a diagonal and E is the mid-point of AD. A line is drawn through E, parallel to AB, intersecting BC at F. Show that F is the mid-point of BC.

Q. Question 1 (vi)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.

Q.

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid - point of AD. A line is drawn through E parallel to AB intersecting BC at F (see the given figure). Show that F is the mid-point of BC.

Q. Question 1 (v)
Does the following figure lie on the same base and between the same parallels? If yes, write the common base and two parallels.