Question

the statements are all converses of theorems. state whether they are true or false.
true
false
if the opposite angles in a quadrilateral are congruent then it is a parallelogram.
if two angles are supplementary then they form a linear pair.
if the diagonals of a quadrilateral are congruent then it is a trapezoid.
if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
if a quadrilateral is a rectangle then it is a square.
if two angles of a triangle are congruent, then the sides opposite them are congruent.

Explanation:

Step1: Recall parallelogram property

A quadrilateral with opposite - angles congruent is a parallelogram. So, "If the opposite angles in a quadrilateral are congruent then it is a parallelogram" is True.

Step2: Recall supplementary and linear - pair relationship

Two supplementary angles don't necessarily form a linear pair. A linear pair of angles are adjacent and supplementary. So, "If two angles are supplementary then they form a linear pair" is False.

Step3: Recall trapezoid and diagonal property

A quadrilateral with congruent diagonals is not necessarily a trapezoid. For example, a rectangle has congruent diagonals. So, "If the diagonals of a quadrilateral are congruent then it is a trapezoid" is False.

Step4: Recall parallel - line and corresponding - angle relationship

If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel (corresponding - angles postulate). So, "If two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel" is True.

Step5: Recall rectangle and square relationship

A rectangle is not necessarily a square. A square has all sides equal, while a rectangle only has opposite sides equal. So, "If a quadrilateral is a rectangle then it is a square" is False.

Step6: Recall triangle congruence property

In a triangle, if two angles are congruent, then the sides opposite them are congruent (isosceles - triangle theorem). So, "If two angles of a triangle are congruent, then the sides opposite them are congruent" is True.

Answer:

1. True
2. False
3. False
4. True
5. False
6. True