Question

properties of parallelograms
opposite sides are _______________.
opposite _______________ are congruent.
consecutive angles are _______________.
the diagonals _______________ each other.

Explanation:

Step1: Analyze the first property

In a parallelogram, by definition, opposite sides have the same length. So, when we see \(\overline{FG}\cong\overline{HJ}\) and \(\overline{GH}\cong\overline{JF}\), the word for the first blank is "congruent".

Step2: Analyze the second property

We are given \(\angle F\cong\angle H\) and \(\angle G\cong\angle J\). These are pairs of opposite angles in the parallelogram. So, the second blank is "angles".

Step3: Analyze the third property

We know that \(m\angle F + m\angle G=180^{\circ}\), \(m\angle G + m\angle H = 180^{\circ}\), \(m\angle H + m\angle J=180^{\circ}\), and \(m\angle J + m\angle F=180^{\circ}\). Two angles whose measures add up to \(180^{\circ}\) are called supplementary angles. So, the third blank is "supplementary".

Step4: Analyze the fourth property

We have \(\overline{FP}\cong\overline{HP}\) and \(\overline{GP}\cong\overline{JP}\). This means that the point \(P\) divides each diagonal into two equal parts. When a line segment (a diagonal in this case) is divided into two equal - length segments by another line segment (the other diagonal), we say that the diagonals "bisect" each other. So, the fourth blank is "bisect".

Answer:

1. congruent
2. angles
3. supplementary
4. bisect