Question
In triangles ABC and CDE, if AC = CE, BC = CD, $\angle\text{A}=60^\circ,\angle\text{C}=30^\circ$ and $\angle\text{D}=90^\circ.$ Are two triangles congruent?
✓
Answer
For the triangles ABC and ECD, we have the following information and corresponding figure:
$\text{AC}=\text{CE}$
$\text{BC}=\text{CD}$
$\angle\text{}A=60^\circ$
$\angle\text{C}=30^\circ$
$\angle\text{D}=90^\circ$
In triangles ABC and ECD, we have
$\text{AC}=\text{EC}$
$\text{BC}=\text{CD}$
and $\angle\text{BAC}=\angle\text{CED}$
The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
$\text{AC}=\text{CE}$
$\text{BC}=\text{CD}$
$\angle\text{}A=60^\circ$
$\angle\text{C}=30^\circ$
$\angle\text{D}=90^\circ$
In triangles ABC and ECD, we have
$\text{AC}=\text{EC}$
$\text{BC}=\text{CD}$
and $\angle\text{BAC}=\angle\text{CED}$
The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
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