Extending BPT for Relation between Bases of Two Triangles

Q.

In the given figure $\Delta ABC\sim \Delta ADE$. If AE : EC = 4 : 7. If x is the length of perpendicular from A to DE, find the length of the perpendicular from A to BC in terms of 'x'.

1. $\frac{15}{4}x$

2. $\frac{13}{4}x$

3. $\frac{9}{4}x$

4. $\frac{11}{4}x$

Q. In the given figure, BA ⊥ AC, DE ⊥ DF such that BA = DE and BF = EC. Show that $\Delta$ ABC $\cong$ $\Delta$ DEF

Q.

In $\Delta$ ABC, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

1. DE intersects AC outside $\Delta$ ABC

2. DE is parallel to BC

3. DE is parallel to AC

4. DE intersects AC inside $\Delta$ ABC

Q. In which of the following figure, the triangle formed by the line segment DE using the sides of the triangle ABC is similar to the triangle ABC?

1. 
2. 
3. 
4. 

Q.

In the$\Delta$ABC, if DE divides AB and AC in the same proportions, then:

1. AD = AE

2. AD = DB

3. DE and BC are parallel

4. DE is half of BC.

Q.

$\text{In the figure given below, point D divides}\text{AB in the ratio 3 : 5 and DE is parallel to}\text{BC. If AE = 4.8 cm, then find the}\text{length of AC.}$

1. $4.8cm$

2. $12cm$

3. $12.8cm$

4. $8.8cm$

Q. $\text{ABCD is a parallelogram with diagonal}\text{AC. If a line XY is drawn such that it cuts}\text{the side AD at point Z and XY || AB, then find the}\text{value of}\frac{BX}{XC}.$

Q.

D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 4.8 cm. AD = 1.6 cm. AC = 4.2 cm and AE = 1.4 cm. Then $DE\parallel BC$.

1. True

2. False

Q. In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.

Q.

In the figure given below, if BC $\parallel$ EF and FG $\parallel$ CD. $\frac{AE}{AB}$ =

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

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

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

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

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

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

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

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

Q. D and E are respectively the points on the sides AB and AC of a $\Delta ABC$ such that AB = 4.8 cm. AD = 1.6 cm. AC = 4.2 cm and AE = 1.4 cm. Then prove that $DE\parallel BC$.

Q.

In the following figure, DE||AC and DC||AP; then $\frac{BE}{EC}=$ ___

1. $\frac{BC}{EC}$

2. $\frac{BC}{AC}$

3. $\frac{BC}{CP}$

4. $\frac{BD}{AC}$

Q. A line drawn parallel to one side of a triangle divides the other two sides in ___ .

1. the same ratio
2. the ratio 1:2
3. the ratio 1:3
4. different ratios

Q. $ABC$ is a triangle and $DE$ is drawn parallel to $BC$ cutting the other sides at $D$ and $E$. If $AB=3.6cm,AC=2.4cm$ and $AD=2.1cm$, then $AE$ = ______.

1. $1.8cm$
2. $1.4cm$
3. $1.2cm$
4. $1.05cm$

Q.

ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that XZ $\parallel$ AB then $\frac{BX}{XC}$ =?

1. $\frac{AY}{AC}$

2. $\frac{DZ}{AZ}$

3. $\frac{AZ}{ZD}$

4. $\frac{AC}{AY}$