# Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.12210203322.jpg

Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Theorem.

You can still ask an expert for help

## Want to know more about Congruence?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Brittany Patton

Step 1
To make the triangle congruent by using the SAS congruence,
First naming the edges and vertex of the triangle,

Step 2
By using sum of interior angle property in $\mathrm{△}ABC\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}DEF$,
$\mathrm{\angle }ABC={180}^{\circ }-\left(\mathrm{\angle }ABC+\mathrm{\angle }BAC\right)$
$\mathrm{\angle }DEF={180}^{\circ }-\left(\mathrm{\angle }EDF+\mathrm{\angle }DFE\right)$
it is given that,
$\mathrm{\angle }ACB=\mathrm{\angle }EDF={90}^{\circ }$ (given)...(i)
$\mathrm{\angle }BAC=\mathrm{\angle }DFE\left(given\right)$...(ii)
Adding equation (i) and (ii) and subtracting them form ${180}^{\circ }$ in both sides,
${180}^{\circ }-\left(\mathrm{\angle }ACB+\mathrm{\angle }BAC\right)={180}^{\circ }-\left(\mathrm{\angle }EDF+\mathrm{\angle }DFE\right)$
$\mathrm{\angle }ABC=\mathrm{\angle }DEF$
Now, in $\mathrm{△}ABC\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}DEF$,
AB=EF(given)
$\mathrm{\angle }ABC=\mathrm{\angle }DEF$(Proved above)
BC=DE(given)
$\mathrm{△}ABC\stackrel{\sim }{=}\mathrm{△}DEF$ (By SAS Congruence Theorem)
Yes, the provided information is enough to prove the triangle congruent by SAS.