Question
In a $\triangle\text{ABC, D}$ and E are points on the sides AB and AC respectively. For the following cases show that DE || BC:
AB = 5.6cm, AD = 1.4cm, AC = 7.2 and AE = 1.8cm.
AB = 5.6cm, AD = 1.4cm, AC = 7.2 and AE = 1.8cm.
✓
Answer
Given AB = 5.6cm, AD = 1.4cm, AC = 7.2cm and AE = 1.8cm
Now, $\frac{\text{AD}}{\text{AB}}=\frac{1.4}{5.6}=\frac{1}{4}$
And, $\frac{\text{AE}}{\text{AC}}=\frac{1.8}{7.2}=\frac{1}{4}$
$\therefore\frac{\text{AD}}{\text{AB}}=\frac{\text{AE}}{\text{AC}}$
Thus, DE divides sides AB and AC of $\triangle\text{ABC}$ in the same ratio. Therefore, by converse of basic proportionality theorem, we have DE || BC.
Now, $\frac{\text{AD}}{\text{AB}}=\frac{1.4}{5.6}=\frac{1}{4}$
And, $\frac{\text{AE}}{\text{AC}}=\frac{1.8}{7.2}=\frac{1}{4}$
$\therefore\frac{\text{AD}}{\text{AB}}=\frac{\text{AE}}{\text{AC}}$
Thus, DE divides sides AB and AC of $\triangle\text{ABC}$ in the same ratio. Therefore, by converse of basic proportionality theorem, we have DE || BC.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The following are quadratic equations in x?$(2x + 3)(3x + 2) = 6(x - 1)(x - 2)$
→In figure, ABC and DBC are two triangles on the same base $B C$. If $A D$ intersects $B C$ at $O$, show that
$
\frac{\operatorname{ar}(\triangle ABC)}{\operatorname{ar}(\triangle DBC)}=\frac{AO}{DO}
$
→$
\frac{\operatorname{ar}(\triangle ABC)}{\operatorname{ar}(\triangle DBC)}=\frac{AO}{DO}
$
Reeti prepares a Rakhi for her brother Ronit. The Rakhi consists of a rectangle of length $8 \ cm$ and breadth $6 \ cm$ inscribed in a circle as shown in the figure. Find the area of the shaded region. $($Use $\pi=3 \cdot 14 )$
→"The product of two consecutive positive integers is divisible by 2". Is this statement true or false? Give reasons.
In Fig. AD and CE are two altitudes of $\triangle ABC$ intersect each other at point F . Prove that $\Delta F D C \sim \Delta B E C$
→PQRS is a trapezium with $P Q \| S R$. If $M$ and $N$ are two points on the non-parallel sides PS and QR respectively, such that MN is parallel to PQ , then show that $\frac{ PM }{ MS }=\frac{ QN }{ NR }$.
→Find the smallest positive rational number by which $\frac{1}{7}$ should be multiplied so that its decimal expansion terminates after 2 places of decimal.
→Find the length of the arc of a circle which subtends an angle of $60^{\circ}$ at the centre of the circle of radius 42 cm .
→Find the mode of the following distribution:
|
Class-interval
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
70-80
|
|
Frequency
|
5
|
8
|
7
|
12
|
28
|
20
|
10
|
10
|
If $\sin X+\sin ^2 X=1,$ prove that $\cos ^2 X+\cos ^4 X=1$.
→