Chapter 9, Problem 1CT

To determine

To classify: the given statement as true or false.

Answer to Problem 1CT

The above statement is False.

Explanation of Solution

Given information:

Opposite angles of an inscribed quadrilateral must be congruent.

Calculation:

Consider the statement:

“Opposite angles of an inscribed quadrilateral must be congruent”.

The diagonals of an inscribed quadrilateral form with sides pairs of congruent angles. If the quadrilateral is $ABCD$ then,

$\angle BAC$ congruent with $\angle CDB$

1. ,
$\angle ABD$ congruent with $\angle DCA$
2. ,
$\angle DAC$ congruent with $\angle CBD$
3. ,
$\angle ADB$ congruent with $\angle BCA$
4. ,
Since,

  $\begin{array}{c}\angle BAD+\angle ADB+\angle ABD=180°\\ \angle BAC+\angle CAD=180°-\angle ADB+\angle ABD\end{array}$

Therefore,

  $\angle BAD\ne \angle BCD$

Hence, from the explanation, the above statement is False.