Which lines, if any, must be parallel based on the given information? Justify your conclusion. Given: ∠3 is congruent to∠13 A.) a||b, Converse of the Alternate Interior Angles Theorem B.) Not enough information to make a conclusion C.) c||d, Converse of the Corresponding Angles Postulate D.) c||d, Converse of the Same-Side Interior Angles Theorem (Post Picture Below)
On the given diagram, mark the angles given to be congruent. These angles are formed by two lines and one transversal. So, "erase" any other lines that do not form these angles. See attachment.
If any lines are parallel, which two will it be?
@Skylarxoxo I cannot help if you are not willing to participate in the discussion. Just saying.
Sorry, @Directrix I was trying to see if I could figure out the answer, I think it is A... The two parallel lines are a and b?
That is correct. The next question is the reason that we know that a is parallel to b. What do you think?
What is the name given to angles like angles 3 and 13 when they appear in parallel situations. Say, are they corresponding angles?
Or, Same-Side Interior Angles, or Alternate Interior Angles
I have no idea as to the reason it is parallel. And, I think it's called alternate interior angles...
Yes, they are alternate interior angles.
Converse of the Corresponding Angles Theorem. If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. ---------------- Alternate Interior Angles Theorem: If two parallel lines are cut by a transversal, then alternate interior angles formed are congruent.
Read that ^^, look at the answer options. What do you think is the correct answer?
One of the options IS correct. Look again.
A.) a||b, Converse of the Alternate Interior Angles Theorem
Correct.
Thank you for your help :)
You are welcome.
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