Application of BPT

Q. In a triangle ABC, D and E are points on sides AB and AC respectively such that, DE||BC. Then $\frac{AD}{AB}$ =.

1. $\frac{AC}{EC}$
2. $\frac{AE}{AC}$
3. $\frac{EC}{AE}$

Q.

If a line intersects sides AB and AC of a $△ABC$ at D and E respectively and is parallel to BC, then $\frac{AD}{AB}$ = $\frac{AE}{x}$ Then $x$ is

____.

1. AC

2. AD

3. AB

4. AE

Q.

In the given figure, $AB\parallel DC$, BO = 6 cm and DO = 8 cm; find $BP\times DO$

1. $42{\text{cm}}^2$

2. $46{\text{cm}}^2$

3. $48{\text{cm}}^2$

4. $52{\text{cm}}^2$

Q.

D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Then, $DE\parallel BC$.

1. True

2. False

Q.

In the given figure $AB\parallel EF\parallel DC$; AB = 67.5 cm. DC = 40.5 cm and AE = 52.5 cm. Find the length of EF.

1. $15\frac{5}{16}\text{cm}$.

2. $25\frac{5}{16}\text{cm}$.

3. $8\frac{5}{16}\text{cm}$.

4. $20\frac{5}{16}\text{cm}$.

Q.

In fig., If PQ $\parallel$ BC and PR $\parallel$CD. Then, $\frac{AR}{AD}$= $\frac{AQ}{AB}$.

Q. In the adjoining figure, ABCD is a $|{|}^{gm}$ whose diagonals AC and BD intersect at O. A line segment through O meets AB at P and DC at Q. Prove that ar(APQD) $=\frac{1}{2}$ar(ABCD).

Q. Question 1 (i)
In the following figure (i), DE || BC. Find EC.

Q.

$\text{If LM || AB, AL = 2x - 4, AC = 4x,}\text{BM = x - 2 and BC = 2x + 3 with x >0,}\text{then x is:}$

1. $\frac{4}{5}units$

2. $5units$

3. $\frac{5}{4}units$

4. $2units$

Q. In $\Delta ABC,AB=9cm,AC=15cm$ and $DE||BC.$ If $\frac{AB}{AD}=3$, sort in ascending order of length.

1. $AD$
2. $DB$
3. $AE$
4. $EC$

Q. In $\Delta$ ABC, AC = 15 cm and DE ll BC. If $\frac{AD}{DB}=\frac{1}{2}$, then AE =___

1. 5 cm
2. 10 cm
3. 7.5 cm
4. 12.5 cm

Q.

In the given figure, PQ is parallel to MN. If $\frac{KP}{PM}=\frac{4}{13}$ and KN = 20.4 cm. Find KQ.

1. 6 cm

2. 5.6 cm

3. 4.8 cm

4. 9.2 cm

Q. In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).

Q.

In the given figure, $\frac{DE}{BC}$, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm. Select the statements that hold true.

1. ME = 3.75 cm, DM = 15 cm

2. ME = 3.75 cm, DM = 12 cm

3. ME = 4 cm, DM = 10 cm

4. ME = 3.25 cm, DM = 15 cm

Q.

In fig., If PQ $\parallel$ BC and PR $\parallel$CD. Then, $\frac{AR}{AD}$= $\frac{AQ}{AB}$.

1. True
2. False

Q.

If PQRS is a parallelogram, with point A on QR, then $\frac{AP}{AB}$ is equal to

1. 2

2. 1

3. can't be determined

4. $\frac{1}{2}$

Q. In Figure, ABC and ABD are two triangles on the same base AB. If line- segment CD is bisected by AB at O, show that: ar(ABC) = ar(ABD).

Q. if -x>0, then which of the following can not be the value of x?

1. 2
2. -1
3. -2
4. -3

Q.

In the given figure $AB\parallel EF\parallel DC$; AB = 67.5 cm. DC = 40.5 cm and AE = 52.5 cm. Find the length of EF.

Q. In $\Delta$ ABC, AC = 15 cm and DE$\parallel$ BC. If $\frac{AB}{AD}=3$, find EC.

1. 5 cm
2. 10 cm
3. 2.5 cm
4. 9 cm

Q.

$\text{If}BC||EF\text{and}FG||CD\text{then,}\frac{AE}{AB}=$ _____.

1. $\frac{AG}{GD}$

2. $\frac{GD}{AG}$

3. $\frac{AG}{AD}$

4. $\frac{CF}{AF}$

Q. $\text{In the given figure,}DE||AC,DC||AP,BC=4\text{cm}\text{and}BP=6\text{cm}.$

$\text{Find the value of}\frac{BE}{EC}.$

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

Q.

In the figure, if $ LM \left|\right| CB$ and $ LN \left|\right| CD$, prove that $ \frac{AM}{AB}=\frac{AN}{AD}$

Q. In $△XYZ,XY=4cm,YZ=6cm,XZ=5cm$. If $\Delta XYZ\sim \Delta PQR$ and $PQ=8cm$, then find the lengths of remaining sides of $△PQR$.

Q. if -x>0, then which of the following can not be the value of x?

1. -1
2. 2
3. -3
4. -2

Q. If you are asked to construct $△$APQ $\sim$ $△$ABC with the scale factor $\frac{3}{5}$, which of the following is incorrect?
Given: In $△ABC,AB=4cm$, $BC=3cm$ and $\angle ABC={90}^{\circ }$.
$A_1{A}_2=A_2{A}_3=A_3{A}_4=A_4{A}_5$.​​​​​​

1. $\angle AQP=\angle ACB$
2. $\angle A{A}_{3}P=\angle A{A}_{5}P$
3. $AP:PB=3:2$
4. 5PQ = 3BC