Question

Given: ∠2and∠4 are vertical angels
Proven: ∠2≅∠4

Answer 1

To prove that angles 2 and 4 are congruent when they are vertical angles, we simply use the basic geometrical property that vertical angles are always congruent. As they share the same vertex and are opposite each other, by definition, angle 2 is congruent to angle 4.

Step-by-step explanation:

• The student's question is asking to prove that angles 2 and 4 are congruent if they are vertical angles. By definition, vertical angles are the angles opposite each other when two lines cross.
• They are called 'vertical' because they share the same vertex.
• Vertical angles are always congruent, which means they have the same measure. Therefore, if ∠2 and ∠4 are vertical angles, then it is a proven fact that ∠2≅∠4, or ∂/2 is congruent to ∂/4.
• This fact about vertical angles being congruent is a fundamental property in geometry that is used to solve various problems.