Question

If $\Delta DEF\cong \Delta RST,m\angle D=100$and $m\angle F=40$. Name four congruent angles.

Short answer

The four congruent angles are $\mathit{m}\mathbf{\angle }\mathit{R}\mathbf{=}\mathbf{100}\mathbf{,}\mathit{m}\mathbf{\angle }\mathit{E}\mathbf{=}\mathbf{40}\mathbf{,}\mathit{m}\mathbf{\angle }\mathit{S}\mathbf{=}\mathbf{40}\mathit{a}\mathit{n}\mathit{d}\mathit{m}\mathbf{\angle }\mathit{T}\mathbf{=}\mathbf{40}$.

Step-by-step solution

Step 1. Apply the concept of congruent triangles.

For the congruent triangles their corresponding sides and angles are equal.

Step 2. Step description.

Consider that $\Delta DEF\cong \Delta RST$, $m\angle D=100$and $m\angle F=40$.

In $\Delta DEF$, $m\angle D=100$and $m\angle F=40$.

Therefore, from angle sum property

$\begin{array}{c}m\angle E=180-\left(100+40\right)\\ =180-140\\ =40\end{array}$

Therefore $\Delta DEF\cong \Delta RST$

Step 3. Step description.

As the congruent triangles their corresponding sides and angles are equal. Thus $D\leftrightarrow R$, $E\leftrightarrow S$, $F\leftrightarrow T.$

Therefore, the four congruent angles are as follows

$m\angle R=100,m\angle E=40,m\angle S=40andm\angle T=40$