Question

3
drag each label to the correct location on the chart.
given: ( angle 1 cong angle 3 )
prove: ( angle 3 cong angle 4 )
diagram of intersecting lines forming angles 1, 2, 3, 4
complete the flow chart to prove ( angle 3 cong angle 4 ).
labels: ( angle 3 cong angle 4 ), ( angle 1 cong angle 2 ), ( angle 1 cong angle 3 ), ( angle 2 cong angle 4 )
flow chart with steps including \vertical angles theorem\, \transitive property of congruence\, \given\ and boxes for angle congruences

Explanation:

Step1: Fill given premise

The "given" box corresponds to the provided information: $\angle 1 \cong \angle 2$

Step2: Apply vertical angles theorem

$\angle 1$ and $\angle 3$ are vertical angles, so by vertical angles theorem: $\angle 1 \cong \angle 3$

Step3: Use transitive property (1)

From $\angle 1 \cong \angle 2$ and $\angle 1 \cong \angle 3$, transitive property gives: $\angle 2 \cong \angle 3$

Step4: Apply vertical angles theorem (2)

$\angle 2$ and $\angle 4$ are vertical angles, so: $\angle 2 \cong \angle 4$

Step5: Use transitive property (2)

From $\angle 2 \cong \angle 3$ and $\angle 2 \cong \angle 4$, transitive property gives: $\angle 3 \cong \angle 4$

Answer:

1. Given box: $\angle 1 \cong \angle 2$
2. Vertical angles theorem box (left): $\angle 1 \cong \angle 3$
3. Final box (right): $\angle 3 \cong \angle 4$