Question

lesson 13 homework

1. fill in the chart below.

properties of parallelograms
opposite sides are
fg ≅ hj
gh ≅ jf

opposite
∠f ≅ ∠h
∠g ≅ ∠j
are congruent.

consecutive angles are
m∠f + m∠g = 180°
m∠g + m∠h = 180°
m∠h + m∠j = 180°
m∠j + m∠f = 180°

the diagonals
fp ≅ hp
gp ≅ jp
each other.

Explanation:

Step1: Recall properties of parallelograms

For a parallelogram, by its definition and proven theorems:

• Opposite angles are congruent. In parallelogram \(OFJH\), \(\angle F\) and \(\angle H\) are opposite angles, \(\angle G\) and \(\angle J\) are opposite angles. So \(\angle F\cong\angle H\) and \(\angle G\cong\angle J\) satisfies the "Opposite angles are congruent" property.
• Opposite sides are congruent. In parallelogram \(OFJH\), \(\overline{FC}\cong\overline{HI}\) and \(\overline{GH}\cong\overline{JF}\) shows the "Opposite sides are congruent" property.
• Diagonals bisect each other. In parallelogram \(OFJH\) with diagonals intersecting (assuming standard parallelogram diagonal property illustration), \(FP = HP\) and \(GP=JP\) means the diagonals bisect each other.
• Consecutive angles are supplementary. In parallelogram \(OFJH\), \(\angle F\) and \(\angle G\) are consecutive angles, \(\angle G\) and \(\angle H\) are consecutive angles, \(\angle H\) and \(\angle J\) are consecutive angles, \(\angle J\) and \(\angle F\) are consecutive angles. So \(m\angle F + m\angle G=180^{\circ}\), \(m\angle G + m\angle H = 180^{\circ}\), \(m\angle H + m\angle J=180^{\circ}\), \(m\angle J + m\angle F=180^{\circ}\) shows the "Consecutive angles are supplementary" property.

Answer:

• Opposite angles are congruent: \(\angle F\cong\angle H\), \(\angle G\cong\angle J\)
• Opposite sides are congruent: \(\overline{FC}\cong\overline{HI}\), \(\overline{GH}\cong\overline{JF}\)
• Diagonals bisect each other: \(FP = HP\), \(GP = JP\)
• Consecutive angles are supplementary: \(m\angle F + m\angle G = 180^{\circ}\), \(m\angle G + m\angle H=180^{\circ}\), \(m\angle H + m\angle J = 180^{\circ}\), \(m\angle J + m\angle F=180^{\circ}\)