this has the same layout of my last question but the given is an angle not a line.
Given:angle 2 and 3 are supplementary and angle 6and 10 are congruent.
prove:m//n
Use this...
Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that two corresponding angles have the same measure, then those lines are parallel.
See what you come up with, and I can critique your thinking.
what is coplanar?
It means "lying in the same plane." In this problem, the lines are coplanar, so you don't have to worry about that part.
Do i need to explain the given?
Yes, start by stating the given information and giving the reason - it's given.
To prove that lines m and n are parallel, we need to demonstrate that the corresponding angles are congruent. In this case, we are given that angle 2 and angle 3 are supplementary, and angle 6 and angle 10 are congruent.
To begin the proof, we will assume the opposite, namely that lines m and n are not parallel. This means that they intersect at some point, let's call it point P.
Now, since lines m and n intersect at point P, we can create several angle pairs. Let's focus on angle 2 and angle 6, which share point P as a vertex and are adjacent to each other.
Since angle 6 and angle 10 are congruent, and m and n intersect at point P, angle 6 and angle 10 can be considered alternate interior angles. By the properties of alternate interior angles, they are congruent.
Now, since angle 2 and angle 6 are adjacent angles, and angle 6 and angle 10 are congruent, we can conclude that angle 2 and angle 10 are also congruent by the Transitive Property of Congruence.
Let's consider angle 3, which is supplementary to angle 2. If angle 2 and angle 10 are congruent, then angle 10 and angle 3 must also be congruent by the Transitive Property of Congruence.
Now, we have that angle 10 is congruent to both angle 3 and angle 6. However, if angles 10 and 6 are congruent, and angles 10 and 3 are congruent, then angles 3 and 6 must also be congruent by the Transitive Property of Congruence.
But this is a contradiction, as angle 3 and angle 6 cannot be congruent and supplementary at the same time.
Therefore, our assumption that lines m and n are not parallel must be false. Hence, we can conclude that lines m and n must be parallel.