Converse of BPT

Q.

Consider $\Delta$ ABC. If $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is an equilateral triangle.

1. True

2. False

Q.

In the given figure, DE || AC and DC || AP, such that BC = 4 cm and BP = 6 cm, then $\frac{BE}{EC}$ is equal to

1. 1 : 1

2. 1 : 3

3. 1 : 2

4. 2 : 1

Q. In $\Delta ABC,D$ and E are points AC and BC respectively such that DE || AB. If AD = 2x, BE = 2x - 1, CD = x + 1 and CE = x - 1, then find the value of x.

Q. In $\Delta$ ABC, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is triangle.

1. Equilateral
2. Isosceles
3. Right angled
4. Scalene

Q.

Question 2 (ii)
E and F are points on the sides PQ and PR respectively of a $\Delta PQR$. For the following case, state whether EF || QR.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

Q.

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

1. $DE\parallel BC$

2. AE = AD

3. $\angle ADE=\angle ACB$

4. DE = BD

Q.

If $a\left|\right|b$ $m\angle 2=63$and $m\angle 9=105$, find the measure of each missing angle.

Q. $Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{3}{5}.$ If $AC=5.6cm$, then $EC=$____

1. 3.5 cm
2. 2.5 cm
3. 2 cm
4. 3 cm

Q.

Question 6
In the following figure, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

Q.

Question 5
In the following figure, DE||OQ and DF||OR, show that EF||QR.

Q.

In the figure shown below , if $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is _______ triangle.

1. Scalene

2. Equilateral triangle

3. Right angled triangle

4. Isosceles

Q.

Question 2 (i)
E and F are points on the sides PQ and PR respectively of a $\Delta PQR$. For the following case, state whether EF || QR.
(i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm

Q. $Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{6}{7}.$ If $AC=13cm$, then $EC=$____

1. 14 cm
2. 7 cm
3. 6 cm
4. 21

Q. In the given figure if DE || BC, then find EC.

Q.

In $\Delta$ABC, if DE divides AB and AC in the same ratio, then which of the following options is true?

1. DE is half of BC

2. AD = AE

3. AD = DB

4. DE and BC are parallel

Q. A tower of height 24 m casts a shadow of 50 m and at the same time and on the same side a girl of height 1.8 m casts a shadow. The girl's shadow is of length .

1. 3 m
2. 3.5 m
3. 3.75 m

Q. ABC is a triangle and M & N are points on AB and AC such that MN || BC. Find the given ratios if AM:MB = 2:3.
1. $AN:AC$
2. $AN:NC$
3. $NC:AC$

Q.

$\text{In the figure, PQ || AB. CQ = 4.8 cm,}\text{QB = 3.6 cm and AB = 6.3 cm. If AP = x,}\text{then what is the length of AC in terms of x ?}$

1. $\frac{8}{3}xunits$

2. $\frac{5}{3}xunits$

3. $\frac{4}{3}xunits$

4. $\frac{7}{3}xunits$

Q. In $\Delta$ ABC, $\frac{AD}{DB}=\frac{AE}{EC}$ and $\angle$ ADE = $\angle$ ACB. Then $\Delta$ ABC is a/an

1. equilateral

2. isosceles

3. scalene

4. right angled

Q. $Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{2}{5}.$ If $AC=5.6cm$, then $AE=$____

1. 3 cm
2. 1.6 cm
3. 4 cm
4. 3.5 cm

Q. $Inthe\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{2}{5}.$ If $AC=5.6cm$, then $AE=$____

1. 4 cm
2. 3.5 cm
3. 1.6 cm
4. 3 cm

Q.

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

1. $5cm$

2. $10cm$

3. $2.5cm$

4. $9cm$

Q.

In $\Delta ABC$, point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $\angle AED$.

Q.

In below shown figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is a/an __ triangle.

Q.

$In\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{3}{5}.$ If $AC=5.6cm$, then $AE=$ _____.

1. 2.1 cm

2. 2.4 cm

3. 3.2 cm

4. 3.6 cm

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

1. 1
2. 2
3. $\frac{1}{2}$
4. can't be determined

Q. In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

1. DE = BD
2. ∠ADE = ∠ACB
3. AE = AD
4. DE || BC

Q.

In $\Delta ABC$, point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $\angle AED$.

1. ${70}^{\circ }$

2. ${75}^{\circ }$

3. ${40}^{\circ }$

4. ${65}^{\circ }$

Q.

In the following figure, $\angle AXY=\angle AYX$.

If $\frac{BX}{AX}=\frac{CY}{AY}$, then triangle ABC is isosceles.

1. False

2. True

Q. If $DE\parallel BC$ in $△ABC,AD=1.5cm,BD=3cm$ and $AE=1cm$, then find $EC$ ( in cm ).