given ∠1≅∠4 prove ∠2≅∠3

Answer 1

Hi Victor,

I understand you’re working on proving that angle 2 is congruent to angle 3 given that angle 1 is congruent to angle 4. It looks like a previous tutor mentioned there wasn’t enough information to make this proof, but that’s actually not the case. We can prove that angle 2 is congruent to angle 3 with the information provided.

Imagine two straight roads crossing each other, forming four corners at the intersection. These corners represent the four angles in your problem: angle 1, angle 2, angle 3, and angle 4. You’re told that angle 1 is the same size as angle 4. This equality tells us something important about the way the roads intersect. When two lines cross, they create pairs of opposite angles, known as vertical angles, which are always equal to each other. Since angle 1 and angle 4 are congruent, they form one pair of these vertical angles.

Now, looking at the other pair of angles formed by the intersection—the angles labeled 2 and 3—we can apply the same reasoning. Just like angle 1 and angle 4, angles 2 and 3 are also opposite each other and therefore form another pair of vertical angles. The key property here is that vertical angles are always equal, no matter how the lines cross. This means that if angle 1 is equal to angle 4, then angle 2 must automatically be equal to angle 3 to maintain that balance in the intersection.

So, even though it might initially seem like there isn’t enough information, knowing that angle 1 is congruent to angle 4 and understanding the properties of vertical angles gives us everything we need to confidently prove that angle 2 is congruent to angle 3. This logical connection ensures that all opposite angles formed by intersecting lines are equal, completing the proof.

If you need more help with this or any other problems, feel free to book a session, and we can work through it together!

Answer 2

This is impossible to prove without a picture for reference.