Question

Hi(: Could some one help me write a paragraph proof ?
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 1

Start with whats given

Answer 2

It is given that \(\angle 1\) and \(\angle 3\) are vertically opposite angles; \(\angle 2\) and \(\angle 4\) are vertically opposite anlges.

Answer 3

thank you (: Should I also write that <1 and <2 are supplementary?

Answer 4

and <2 and <3 are supplementary?

Answer 5

It is given that \(\angle 1\) and \(\angle 3\) are vertically opposite angles; \(\angle 2\) and \(\angle 4\) are vertically opposite anlges. Since AB is a straight angle, \(\angle 1 + \angle 2 = 180\) by linear pair of angles theorem.

Answer 6

wow ! you're brilliant !! yes.... put everything in paragraph form in a logical ORDER..

Answer 7

@ganeshie8 It is given that angle1 and angle3 are vertically opposite angles and angle 2 and angle 4 are vertically opposite angles. Since AB is and straight angle, angle 1 + angle2=180 by the definition of supplementary angles. Angle 2+angle3=180 by the definition of supplementary angles also. So by substitution angle 1equals angle3
Does this sound alright?

Answer 8

looks good, ima modify it a bit..

Answer 9

It is given that angle1 and angle3 are vertically opposite angles and angle 2 and angle 4 are vertically opposite angles. Since AB is a straight angle, angle 1 + angle2=180 by the definition of supplementary angles. Since t is a straight line, Angle 2+angle3=180 by the definition of supplementary angles also. So by transitive property of equality, angle1 + angle2 = angle2+angle3. Thus by subtraction property, angle1 equals angle3.

Answer 10

Yo! You're the best! Thanks :p

Answer 11

aww noo you're the best :) you wlcme :)