Criteria for Congruence of Triangles

Complete the congruence statement using the figure given below.

$△QRS\cong △\_\_\_$

Complete the congruence statement given below.

$△BCA\cong △\_\_\_$

In the figure, two triangles are congruent.

The corresponding parts are marked. We can write $\mathrm{\Delta }\mathrm{R}\mathrm{A}\mathrm{T}\cong ∆\_\_\_$

You want to show that $∆\mathrm{ART}\cong ∆\mathrm{PEN}$. If it is given that $AT=PN$ and you are to use $\mathrm{ASA}$ criterion, you need to have $\mathrm{\angle }T=\mathrm{\angle }N$ and $\mathrm{\angle }A=\mathrm{\angle }$_____?

If it is given that $\mathrm{\angle }\mathrm{T}=\mathrm{\angle }\mathrm{N}$ and you are to use $SAS$ criterion, you need to have $\mathrm{R}\mathrm{T}\mathrm{}=$
 

You want to show that $∆\mathrm{ART}\cong ∆\mathrm{PEN}$, and we have to use $\mathrm{AR}=\mathrm{PE}$, $\mathrm{RT}=\mathrm{EN}$, $\mathrm{AT}=\mathrm{PN}$, then which of the following condition is used. $\left[\mathrm{SSS}/\mathrm{SAS}/\mathrm{ASA}\right]$

In the given figure, $\Delta ABE\cong \Delta CDB$ in which $EB=DB$, $AE=BC$ and $\angle A=\angle C=90°$. Which congruency criteria is used here? $(\mathrm{SSS}$/$\mathrm{SAS}$/$\mathrm{ASA}$/$\mathrm{RHS})$.

Which congruence criterion do you use in the following?

Given: $\mathrm{\angle }\mathrm{M}\mathrm{L}\mathrm{N}=\mathrm{\angle }\mathrm{F}\mathrm{G}\mathrm{H}$, $\mathrm{\angle }\mathrm{N}\mathrm{M}\mathrm{L}=\mathrm{\angle }\mathrm{G}\mathrm{F}\mathrm{H}$, $\mathrm{M}\mathrm{L}=\mathrm{F}\mathrm{G}$. So, $\mathrm{\Delta }\mathrm{L}\mathrm{M}\mathrm{N}\cong \mathrm{\Delta }\mathrm{G}\mathrm{F}\mathrm{H}$.

Choose the correct word from: $\mathrm{ASA}/\mathrm{SSS}/\mathrm{SAS}/\mathrm{AAA}$.

Given, $\mathrm{Z}\mathrm{X}=\mathrm{R}\mathrm{P}$, $\mathrm{Z}\mathrm{Y}=\mathrm{RQ}$, $\angle \mathrm{X}\mathrm{Z}\mathrm{Y}=\mathrm{\angle }\mathrm{PRQ}$, if $\mathrm{\Delta }\mathrm{X}\mathrm{Y}\mathrm{Z}\cong \mathrm{\Delta PQR}$, then which congruence criterion do you use? $\left(\mathrm{ASA}/\mathrm{SAS}/\mathrm{AAA}/\mathrm{SSS}\right)$

Given $\mathrm{A}\mathrm{C}=\mathrm{D}\mathrm{F}$, $\mathrm{A}\mathrm{B}=\mathrm{D}\mathrm{E}$, $\mathrm{B}\mathrm{C}=\mathrm{E}\mathrm{F}$, if $\mathrm{\Delta ABC}\cong \mathrm{\Delta DEF}$, which congruence criterion do you use? $\left(\mathrm{ASA}/\mathrm{SAS}/\mathrm{SSS}/\mathrm{AAA}\right)$

In $\mathrm{\Delta }\mathrm{A}\mathrm{B}\mathrm{C}$, $\mathrm{\angle }\mathrm{A}={30}^{\mathrm{o}}$, $\mathrm{\angle }\mathrm{B}={40}^{\mathrm{o}}$ and $\mathrm{\angle }\mathrm{C}={110}^{\mathrm{o}}$
In $\mathrm{\Delta }\mathrm{P}\mathrm{Q}\mathrm{R}$, $\mathrm{\angle }\mathrm{P}={30}^{\mathrm{o}}$, $\mathrm{\angle }\mathrm{Q}={40}^{\mathrm{o}}$ and $\mathrm{\angle }\mathrm{R}={110}^{\mathrm{o}}$
A student says that $\mathrm{\Delta }\mathrm{A}\mathrm{B}\mathrm{C}\cong \mathrm{\Delta }\mathrm{P}\mathrm{Q}\mathrm{R}$ by $AAA$ congruence criterion. Is he justified? Why or why not?