Question

given: ( jklm ) is a parallelogram.
( angle 2 cong angle 3 )
prove: ( angle 1 cong angle 3 )
drag an expression or phrase to each box to complete the proof.
it is given that ( jklm ) is a parallelogram, so ( overline{jm} parallel overline{kl} ) by the
therefore, ( angle 1 )( cong angle 2 ) by the corresponding angles postulate. also, it is given that ( cong angle 3 ), so ( angle 1 cong )
by the

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are parallel. So, \(JM\parallel KL\) by the definition of a parallelogram.

Step2: Corresponding angles

Since \(JM\parallel KL\), by the corresponding angles postulate, \(\angle1\cong\angle2\).

Step3: Given condition

It is given that \(\angle2\cong\angle3\).

Step4: Transitive property

By the transitive property of congruence (if \(a = b\) and \(b = c\), then \(a = c\)), \(\angle1\cong\angle3\).

Answer:

1. definition of a parallelogram
2. \(\angle2\)
3. \(\angle3\)
4. transitive property of congruence