Question

drag each label to the correct location on the flowchart.
given: line ( l ) and line ( m ) intersect
prove: ( angle 1 cong angle 3 )
complete the proof.
( angle 1 cong angle 3 )( angle 2 ) is supplementary to ( angle 3 )( angle 3 ) is supplementary to ( angle 4 )( angle 2 cong angle 4 )
line ( l ) and line ( m ) intersect given( angle 1 ) is supplementary to ( angle 2 ) linear pair theoremlinear pair theoremcongruent supplements theorem

Explanation:

Step1: Apply linear pair theorem

By linear pair theorem, \(\angle2\) is supplementary to \(\angle3\) (since \(\angle2\) and \(\angle3\) form a linear pair).

Step2: Use congruent supplements theorem

Since \(\angle1\) is supplementary to \(\angle2\) (given by linear - pair theorem for \(\angle1\) and \(\angle2\)) and \(\angle2\) is supplementary to \(\angle3\) (from Step 1), by the congruent supplements theorem (\(\text{If two angles are supplementary to the same angle, then they are congruent}\)), \(\angle1\cong\angle3\)

Answer:

The first blank (linear pair theorem) is filled with \(\angle2\) is supplementary to \(\angle3\). The second blank (congruent supplements theorem) is filled with \(\angle1\cong\angle3\)