Question

Earl and Sean provide the following proofs for vertical angles to be equal.

A line PQ is shown cut by a transversal t. 1, 2, 3, 4 are marked clockwise as the four angles formed by the transversal on the segment PQ

Earl’s proof: angle 1 + angle 2 = 180° (PQ is a straight line)
angle 3 + angle 4 = 180°(PQ is a straight line)
Therefore, angle 1 + angle 2 = angle 3 + angle 4
Hence, vertical angles are equal.

Answer 1

Sean’s proof: angle 1 + angle 4 = 180° (transversal t is a straight line)
angle 2 + angle 3 = 180°(transversal t is a straight line)
Therefore, angle 1 + angle 4 = angle 2 + angle 3
Hence, vertical angles are equal.

Which statement is correct?

Only Earl’s proof is correct.

Both Earl’s and Sean’s proofs are correct.

Only Sean’s proof is correct.

Both Earl’s and Sean’s proofs are incorrect.

Answer 2

Someone please help this is my second to last question

Answer 3

@mathstudent55 can you help?

Answer 4

Where is Sean's proof?

Answer 5

I only see Earl's proof above

Answer 6

I see it now. They're both incorrect.

Answer 7

okay thank you. can you explain why there incorrect tho?

Answer 8

Can you actually help me with one more? @mathstudent55

Answer 9

The figure below shows a straight line AB intersected by another straight line t.

A segment AB is intersected by a transversal labeled t. Angles 1 and 3 and 2 and 4 are vertically opposite angles formed by the transversal on the segment.

Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3.

Answer 10

@mathstudent55