Basic proportionality theorem

Q.

It is given that ∆ ABC ~ ∆ EDF such that $AB=5cm,AC=7cm,DF=15cm$ and $DE=12cm$. Find the lengths of the remaining sides of the triangles.

Q.

Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX) .

Q.

In the figure, $ A$, $ B$ and $ C$ are points on $ OP$, $ OQ$ and $ OR$ respectively such that $ AB \left|\right| PQ$ and $ AC \left|\right| PR$.

Show that $ BC \left|\right| QR$

Q.

In $△$ABC, AB = 3 and, AC = 4 cm and AD is the bisector of $\angle$A. Then, BD : DC is —

1. 4:3

2. 16:9

3. 3:4

4. 9:16

Q.

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

1. 3.6 cm

2. 2.1 cm

3. 2.4 cm

4. 3.2 cm

Q. In $\Delta ABC$, AC = 15 cm and DE || 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.

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

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

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

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

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

Q.

In ABC , Given that DE//BC , D is the midpoint of AB and E is a midpoint of AC. The ratio AE : EC is ____.

1. 1:1

2. 1:2

3. None of the above

4. 2:1

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

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

Q. In $\Delta ABC$, if D and E are midpoints of AB and BC respectively, then $\frac{AD}{DB}$= ___$\times$ $\frac{BE}{EC}$

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

Q.

In triangle ABC, D is a point on AB and E is a point on AC such that DE || BC. If $\frac{AD}{AB}$ = $\frac{AE}{x}$, Then $x$ is

___.

Q. In the adjoining figure, $D$ is a point on $BC$ such that $\angle ABD=\angle CAD$. If $AB=5cm,AC=3cm$ and $AD=4cm$, find
(i) $BC$
(ii) $DC$
(iii) area of $△ACD$: area of $△BCA$.

Q.

$\text{ABCD is a parallelogram with diagonal}\text{AC. If a line XY is drawn such that it cuts}\text{the side AD at point Z and XY || AB, then}\frac{BX}{XC}\text{can be equal to:}$

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

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

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

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

Q. In $\Delta ABC$, DE || BC. Then which of the following is stated by Basic Proportionality Theorem?

1. $\frac{AB}{DB}=\frac{EC}{AC}$
2. $\frac{AD}{DB}=\frac{AE}{EC}$
3. $\frac{AB}{DB}=\frac{AE}{EC}$
4. $\frac{AD}{DB}=\frac{AC}{EC}$