Download App

Triangles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTriangles3 Marks
Question
In a $\triangle\text{ABC, D}$ and $E$ are points on the sides $AB$ and $AC$ respectively. For the following cases show that $DE || BC:$
$AB = 12\ cm, AD = 8\ cm, AE = 12\ cm$ and $AC = 18\ cm.$
✓

Answer


$\text{AB} = 12\text{cm}, \text{AD} = 12\text{cm}\ \text{and AC} = 18\text{cm.}$
$\therefore\text{AD}=\text{AB}-\text{AD}$
$=12-8$
$\Rightarrow\text{DB}=4\text{cm}$
$\text{And, EC}=\text{AC}-\text{AE}$
$=18-12$
$\Rightarrow\text{EC}=6\text{cm}$
$\text{Now},\frac{\text{AD}}{\text{DB}}=\frac{8}{4}=\frac{2}{1}\ \ [\because\text{DB}=4\text{cm}]$
$\text{And},\frac{\text{AE}}{\text{EC}}=\frac{12}{6}=\frac{2}{1}\ \ [\because\text{EC}=6\text{cm}]$
$\Rightarrow\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}$
Thus, $DE$ divides sides $AB$ and $AC$ of $\triangle\text{ABC}$ in the same ratio.
Therefore, by the converse of basic proportionality theorem.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Triangles→Triangles — all question types→Maths STD 10 question papers→Gujarat Board STD 10 question papers→Gujarat Board question paper generator→

Similar questions

Find all the zeros of the polynomial $x^3+ 3x^2- 2x - 6,$ if two of its zeros are $-\sqrt{2}$ and $\sqrt{2}.$
→
Given $15 \cot A=8$ find $\sin A$ and $\sec A$.
→
A father is three times as old as his son. After twelve years, his age will be twice as that of his son then. Find their present ages.
→
In a $\triangle\text{ABC, D}$ and $E$ are points on the sides $AB$ and $AC$ respectively. For the following cases show that $DE || BC:$
$AB = 10.8cm, BD = 4.5cm, AC = 4.8cm$ and $AE = 2.8cm.$
→
Two cubes each of volume $64\ cm^3$ are joined end to end. Find the surface area and volume of the resulting cuboid.
→
In $\triangle\text{ABC},\ \angle\text{A}$ is obtuse, $\text{PB}\perp\text{AC}$ and $\text{QC}\perp\text{AB}$ Prove that:
$AB × AQ = AC × AP$
→
In a hospital used water is collected in a cylindrical tank of diameter $2\ m$ and height $5\ m.$ After recycling, this water is used to irrigate a park of hospital whose length is $25\ m$ and breadth is $20\ m.$ If tank is filled completely then what will be the height of standing water used for irrigating the park.
→
In $\triangle\text{ABC},$ if $\text{BD}\perp\text{AC}$ and $BC^2= 2AC × CD,$ then prove that $AB = AC.$
→
Two poles of heights $6m$ and $11m$ stand on a plane ground. If the distance between their feet is $12m,$ find the distance between their tops.
→
Show that the sequence defined by $a_n=3 n^2-5$ is not an $A.P.$
→