Chapter 3.CT, Problem 1CT

	It is given that $\Delta ABC\cong \Delta DEF$ (triangles not shown)
	a)	If $\text{m}\angle A=\text{37}°$ and $\text{m}\angle E=68°$, find $\text{m}\angle F$.
	b)	If $AB=7.3\text{cm}$, $BC=4.7\text{cm}$, and $AC=6.3\text{cm}$, find $EF$.

To determine

a)

To find:

The value of $\text{m}\angle F$.

Answer to Problem 1CT

Solution:

The value of $\text{m}\angle F$ is $75°$.

Explanation of Solution

The measure of sum of angles of a triangle is equal to $180°$.

Given:

$\Delta ABC\cong \Delta DEF$, $\text{m}\angle A=\text{37}°$

And,

$\text{m}\angle E=68°$

Calculation:

In $\Delta ABC$ and $\Delta DEF$,

$\begin{array}{rll}\text{m}\angle A& =& \text{m}\angle D\\ & =& 37°\end{array}$

Equate the measure of sum of angles of $\Delta DEF$ is equal to $180°$.

$\text{m}\angle D+\text{m}\angle E+\text{m}\angle F=180°$…$\left(1\right)$

Substitute $37°$ for $\text{m}\angle D$ and $68°$ for $\text{m}\angle E$ in equation $\left(1\right)$ in order to find the value of $\text{m}\angle F$

$\begin{array}{rll}37°+68°+\text{m}\angle F& =& 180°\\ \text{m}\angle F& =& 180°-37°-68°\\ & =& 75°\end{array}$

Conclusion:

Therefore, the value of $\text{m}\angle F$ is $75°$.

To determine

b)

To find:

The value of $EF$.

Answer to Problem 1CT

Solution:

The value of $EF$ is $4.7\text{cm}$.

Explanation of Solution

If two triangles are congruent, then all sides of the triangles are congruent.

Given:

$\Delta ABC\cong \Delta DEF$, $AB=7.3\text{cm}$, $BC=4.7\text{cm}$

And,

$AC=6.3\text{cm}$

Calculation:

In $\Delta ABC$ and $\Delta DEF$,

$BC=EF$

Substitute $4.7\text{cm}$ for $BC$ in above relation in order to get the value of $EF$.

$\begin{array}{rll}4.7\text{cm}& =& EF\\ EF& =& 4.7\text{cm}\end{array}$

Conclusion:

Therefore, the value of $EF$ is $4.7\text{cm}$.