Download App

Triangles — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsTriangles3 Marks
Question
In the figure, $E$ is the point on side $CB$ produced on an isosceles triangle $ABC$ with $AB = AC.$ If $AD \bot BC$ and $EF \bot AC,$ prove that $\triangle ABD \sim \triangle ECF.$
✓

Answer

$E$ is the point on side $CB$ produced on an isosceles triangle $ABC$ with $AB=AC.AD-BC \bot$ and$ EF \bot AC.$ with $AB=AC.$ Also, $AD \bot BC$ and $EF \bot AC.$
To prove:$ \triangle ABD \sim \triangle ECF$
Proof: In $\triangle ABD$ and $\triangle ECF,$
$\therefore AB = AC ........$Given
$\therefore \angle ACB = \angle ABC ......$Angle opposite to equal sides of a triangle are equal
$\Rightarrow \angle ABC = \angle ACB $
$ \Rightarrow \angle ABD = \angle ECF ..........(1)$
$ \angle ADB = \angle EFC .........(2) [$Each equal to $90^\circ$ In view of $(1)$ and $(2)]$
$\triangle ABD \sim \triangle ECF.............AA$ similarity criterion

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

In a circle of radius $10.5\ cm,$ the minor arc is one-fifth of the major arc. find the area of the sector corresponding to the major are. $\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→

If $\cot\theta=\frac{3}{4},$ prove that $\sqrt{\frac{\sec\theta-\text{cosec }\theta}{\sec\theta+\text{cosec }\theta}}=\frac{1}{\sqrt{7}}.$

→
What are the coordinates of the point where the perpendicular bisector of the line segment joining the points $A(1, 5)$ and $B(4, 6)$ cuts the $y-$axis$?$
→
A T.V. Tower stands vertically on a bank of a river. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is $60^\circ .$ From a point $20\ m$ away this point on the same bank, the angle of elevation of the top of the tower is $30^\circ .$ Find the height of the tower and the width of the river.
→
Solve the following question-Aftab tells his daughter, Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be. (Isn’t this interesting?) Represent this situation algebraically and graphically by the method of substitution.
→
The product of Ramu's age $($in years$)$ five years ago and his age $($in years$)$ nine years later is $15$. Determine Ramu's present age.
→
The angle of elevation of the top of the building from the foot of the tower is $30^\circ $ and the angle of the top of the tower from the foot of the building is $60^\circ .$ If the tower is 50m high, find the height of the building.
→
Solve the following quadratic equation:
$ 2 x^2+a x-a^2=0 $
→
Find the sum of the first $15$ terms of each of the following sequences having $n^{th}$ term as:
$b_n= 5 + 2n.$
→
In a $\triangle\text{ABC} D$ and $E$ are points on $AB$ and $AC$ respectively such that $DE || BC.$ If $AD = 2.4\ cm, AE = 3.2\ cm, DE = 2\ cm$ and $BC = 5\ cm,$ find $BD$ and $CE.$
→