In the adjoining figure $AB =AD$ and $CB =CD$ Prove that $\vartriangle ABC\cong\vartriangle ADC$
"
Given: $AB=AD$ and $CB=CD$
To do: To prove that $\vartriangle ABC\cong\vartriangle ADC$
Solution:
In $\vartriangle ABC$ and $\vartriangle ADC$,
$AB=AD$ and $CD=CB$ $( Given)$
$AC=AC$ $( Common)$
So, according to SSS congruency rule,
$\vartriangle ABC\cong\vartriangle ADC$
$\vartriangle ABC$ is congruent to $\vartriangle ADC$.
- Related Articles
- If $AD$ and $PM$ are medians of $\vartriangle ABC$ and $\vartriangle PQR$ respectively where, $\vartriangle ABC\sim \vartriangle PQR$. Prove that $\frac{AB}{PQ}=\frac{AD}{PM}$.
- In the figure, it is given that $AB = CD$ and $AD = BC$. Prove that $\triangle ADC \cong \triangle CBA$."\n
- $O$ is the point of intersection of two equal chords $AB$ and $CD$ such that $OB=OD$, then prove that $\vartriangle OAC$ and $\vartriangle ODB$ are similar."\n
- In figure 2, $\vartriangle$AHK is similar to $\vartriangle$ABC. If AK$=10$ cm\n
- Given $\vartriangle ABC\ \sim\vartriangle PQR$, If $\frac{AB}{PQ}=\frac{1}{3}$, then find $\frac{ar( \vartriangle ABC)}{ar( \vartriangle PQR)}$.
- In the figure, prove that:$CD + DA + AB > BC$"\n
- In the figure, $AD \perp CD$ and $CB \perp CD$. If $AQ = BP$ and $DP = CQ$, prove that $\angle DAQ = \angle CBP$.
- If $\vartriangle ABC\sim\vartriangle QRP$, $\frac{ar( \vartriangle ABC)}{( \vartriangle QRP)}=\frac{9}{4}$, and $BC=15\ cm$, then find $PR$.
- Construct a $\vartriangle ABC$ in which $AB\ =\ 6\ cm$, $\angle A\ =\ 30^{o}$ and $\angle B\ =\ 60^{o}$, Construct another $\vartriangle AB’C’$ similar to $\vartriangle ABC$ with base $ AB’\ =\ 8\ cm$.
- In the figure, prove that:$CD + DA + AB + BC > 2AC$"\n
- In figure, the vertices of $\vartriangle ABC$ are $A( 4,\ 6) ,\ B( 1,\ 5)$ and $C( 7,\ 2)$. A line-segment DE is drawn to intersect the sides AB and AC at D and E respectively such that$\frac{AD}{AB} =\frac{AE}{AC} =\frac{1}{3}$.Calculate the area of $\vartriangle ADE$ and compare it with area of $\vartriangle ABC$."\n
- In Fig. 1, $DE||BC, AD=1\ cm$ and $BD=2\ cm$. What is the ratio of the $ar( \vartriangle ABC)$ to the $ar( \vartriangle ADE)$?"\n
- If $P$ And $Q$ are the points on side $CA$ and $CB$ respectively of $\vartriangle ABC$, right angled at C, prove that $( AQ^{2}+BP^{2})=( AB^{2}+ PQ^{2})$.
- In the given figure, $ABC$ is a triangle in which $\angle ABC = 90^o$ and $AD \perp CB$. Prove that $AC^2 = AB^2 + BC^2 - 2BC \times BD$"
- If $\vartriangle ABC \sim\vartriangle DEF$, $AB = 4\ cm,\ DE = 6\ cm,\ EF = 9\ cm$ and $FD = 12\ cm$, find the perimeter of $ABC$.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
