Question

AO parallel to BQ 2 congruent to 3 prove 1 congruent 4

Answer 1

Parallel lines, transversal cuts, corresponding angles equal, voila!
`$\angle 1 = \angle 4$`.

The diagram shows two sets of parallel lines cut by a transversal. We are given that
`$\angle 2 = \angle 3$` and asked to prove that
`$\angle 1 = \angle 4$`.

Here's how we can approach this:

1. Identify corresponding angles: Since the lines are parallel, we know that
`$\angle 1$` and
`$\angle 3$` are corresponding angles. Similarly,
`$\angle 2$` and
`$\angle 4$` are corresponding angles.

2. Use the given information: We are given that
`$\angle 2 = \angle 3$`.

3. Substitute corresponding angles: Since we know that
`$\angle 1$` and
`$\angle 3$` are corresponding angles, we can substitute
`$\angle 3$` with
`$\angle 1$` in the equation
`$\angle 2 = \angle 3$`. This gives us
`$\angle 2 = \angle 1$`.

4. Repeat for the other pair of corresponding angles: Similarly, since
`$\angle 2$ and $\angle 4$` are corresponding angles, we can substitute
`$\angle 2$` with
`$\angle 4$` in the equation
`$\angle 2 = \angle 1$`. This gives us
`$\angle 4 = \angle 1$`.

5. Conclusion: Therefore, we have proven that
`$\angle 1 = \angle 4$`, as desired.

In other words, if two parallel lines are cut by a transversal, and the corresponding angles on one side are congruent, then the corresponding angles on the other side are also congruent.