Question

problem 24
clear
statements
reasons
given: parallelogram
dfgj, dj > df

1. click here to insert
2. given
3. m∠dfj > m∠djf
4. click here to insert

prove: m∠gjf > m∠djf

1. (overline{fd}paralleloverline{gj})
2. click here to insert

Explanation:

Part 1: Inserting the First Statement

Step1: Identify the Given Information

The first given is "Parallelogram DFGJ, DJ > DF". So the first statement should be "Parallelogram DFGJ, DJ > DF".

Part 2: Reason for \(m\angle DFJ>m\angle DJF\)

Step1: Recall the Isosceles Triangle Theorem (Extended)

In a triangle, if one side is longer than another side, then the angle opposite the longer side is larger. In \(\triangle DFJ\), since \(DJ > DF\), by the side - angle relationship in a triangle (if \(a>b\) in \(\triangle ABC\) where \(a,b\) are side lengths and \(A,B\) are the angles opposite to \(a,b\) respectively, then \(A > B\)), the reason for \(m\angle DFJ>m\angle DJF\) is "In a triangle, the larger side is opposite the larger angle".

Part 3: Reason for \(\overline{FD}\parallel\overline{GJ}\)

Step1: Recall the Property of Parallelograms

One of the properties of a parallelogram is that opposite sides are parallel. Since DFGJ is a parallelogram, \(\overline{FD}\) and \(\overline{GJ}\) are opposite sides. So the reason is "Opposite sides of a parallelogram are parallel".

Answer:

1. Parallelogram DFGJ, DJ > DF
2. In a triangle, the larger side is opposite the larger angle
3. Opposite sides of a parallelogram are parallel