Question
✓
Answer
Given: In the figure, $\triangle ABE \cong \triangle ACD$
To prove: $\triangle ADE \sim \triangle ABC$
Proof:
$\because \triangle ABE \cong \triangle ACD$........[Given]
$\therefore $ AB = AC........[CPCT
AE = AD ........(1)
Also, $\angle$ DAE= $\angle$ BAC.......[Common $\angle$ ].......(2)
In view of (1) and [SAS similarity criterion]
To prove: $\triangle ADE \sim \triangle ABC$
Proof:
$\because \triangle ABE \cong \triangle ACD$........[Given]
$\therefore $ AB = AC........[CPCT
AE = AD ........(1)
Also, $\angle$ DAE= $\angle$ BAC.......[Common $\angle$ ].......(2)
In view of (1) and [SAS 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.
Explore more
Similar questions
An arc of length $15\ cm$ subtends an angle of $45^\circ$ at the centre of a circle. Find in terms of $\pi$, the radius of the circle.
→The following are the roots of $3 x^2+2 x-1=0?$
→Evaluate:
$=\frac{\sin18^\circ}{\cos72^\circ}+\sqrt{3}\ \{\tan10^\circ\tan30^\circ\tan40^\circ\tan50^\circ\tan80^\circ\}$
→$=\frac{\sin18^\circ}{\cos72^\circ}+\sqrt{3}\ \{\tan10^\circ\tan30^\circ\tan40^\circ\tan50^\circ\tan80^\circ\}$
Find the value of k for the quadratic equation $2 x^2+k x+3=0$, so that they have two real equal roots.
→What is a composite number?
On comparing the ratios $\frac { a _ { 1 } } { a _ { 2 } } , \frac { b _ { 1 } } { b _ { 2 } }$ and $\frac {c_1}{c_2}$, find out whether the lines representing the pair of linear equations intersect at a point, are parallel or coincident: $5x – 4y – 8 = 0; 7x + 6y – 9 = 0$.
→In FIg. check whether $AD$ is the bisector of $\angle\text{A}$ of $\triangle\text{ABC}$ in the following.
$AB = 8\ cm, AC = 24\ cm, BD = 6\ cm$ and $BC = 24\ cm.$
→$AB = 8\ cm, AC = 24\ cm, BD = 6\ cm$ and $BC = 24\ cm.$
$S$ and $T$ are points on sides $PR$ and $QR$ of $\triangle PQR$ such that $\angle P = \angle R T S$. Show that $\triangle R P Q \sim \triangle R T S$.
→Find the $LCM$ and $HCF$ of the following integer by applying the prime factorisation method.
$17, 23$ and $29$
→$17, 23$ and $29$
Solve the following quadratic equation:
$\text{x}^2-\big(\sqrt3+1\big)\text{x}+\sqrt3=0$
→$\text{x}^2-\big(\sqrt3+1\big)\text{x}+\sqrt3=0$