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# if a transversal intersects two parallel lines then

From Wikipedia

Transversal line

In geometry, a transversal line is aline that passes through two or more other coplanar lines at different points.

In Euclidean geometry if lines a and b are parallel, and line t intersects lines a and b, then corresponding angles formed by line t and the parallel lines are congruent.

## Alternate angles

A transversal line is a line that transverses other lines

## Theorems

There are at least eight geometrical theorems concerning transversals. They are as follows:

Theorem 9 If a transversal intersects two parallel lines, then the alternate interior angles are congruent.

Theorem 10 If a transversal intersects two parallel lines, then the corresponding angles are congruent.

Theorem 11 If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.

Theorem 12 If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary.

The next four theorems are converses of the previous four theorems.

Theorem 13 If a transversal intersects two lines so that alternate interior angles are congruent, then the lines are parallel.

Theorem 14 If a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.

Theorem 15 If a transversal intersects two lines so that alternate exterior angles are congruent, then the lines are parallel.

Theorem 16 If a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

### Proofs

#### Theorem 9

thumb|center|500px|

Given: y ll z; transversal t intersects line y and z at A and B; O is the midpoint of lineSEGMENTAB.

Prove: angle 1 is congruent to angle 3; angle 2 is congruent to angle 4.

1. y ll z; transversal intersects lines y and z at A and B; O is the midpoint of line AB.

2. Through O, draw line CD perpendicular to z.(P. means Postulate)

3. Line CD is perpendicular to y.(T. means Theorem)

4. Angle ACO and BDO are right angles.

5. Î”ACO and BDO are right triangles.

6. Angle 5 is congruent to angle 6.

7. Line AO is congruent to line BO.

8. âˆ´ Î”ACO is congruent to Î”BDO.

9. âˆ´ Angle 1 is congruent to angle 3.

10. Angle 2 is supplementary to angle 1; angle 4 is supplementary to angle 3.

11. âˆ´ Angle 2 is congruent to angle 4.

#### Theorem 11

thumb|center|500px|Theorem 11 Formal Proof Image.Given: Transversal t intersects lines m and n; m ll n.

Prove: Angle 1 is congruent to angle 7.

1. Transversal t intersects lines m and n; m ll n.

2. Angle 3 is congruent to angle 5.

3. Angle 1 is congruent to angle 3; angle 5 is congruent to angle 7.

4. âˆ´ Angle 1 is congruent to angle 7.

#### Theorem 12

Given: Transversal t intersects lines m' and n; m ll n.

Prove: Angle 1 is supplementary to angle 2.

1. Transversal t intersects lines m and n ; m ll n.

2. Angle 2 is congruent to angle 3.

3. Angle 1 is supplementary to angle '3.

4. âˆ´ Angle 1 is supplementary to angle 2.

Question:If two parallel lines are intersected by a transversal the alternate angles are? if two parallel lines are intersected by a transversal the co-interior angles are?

Question:Ok so i have a math poster kind of thing due and its on parallel lines and transversals as seen in the title and im not to sure understanding how to do these my job in my group is to explain how to answer the questions with these in them and my other group members are getting the questions drawing the diagrams so id someone could help me id appreacate it because all the iternet sites ive been too are too confusing Best answer 5 stars!

Answers:on ur poster draw two lines going diagonal and don't touch. than below that draw another se twith a line through it. Explain the parralle lines never touch and contine on forevre without touching. also explain that they always stay the exact distance apart. than explain the a transversal line intersects two parrale lines. explin that the lines still are the same distance away but have a line through them. and lastly were the lines intersect angles are formed.

Question:If two parallel lines are cut by a transversal, how do alternate interior angles compare?

Answers:if a transversal intersects two parallel lines then alternate angles are equal and the interior angles on the same side of the transversal are supplementary i.e. their sum is 180 degrees answer!!!!!!!!!

Question:Lets say you have two parallell lines-AB and CD. These two lines are cut by a transversal AED and transversal BED. Now you have two triangles. Triangle AEB and triangle EDC. BE equals 1. CD equals 5, CE equals 3 and AD equals 7. How do you find the lengths of the other pieces? I know you should set up proportions but it doesnt seem like there is enough information to do that. thanks!

Answers:This doesn't look right. A line is defined by two points. So the lines AED and BED should be the same line since they both have the points E and D. But line AB intersects line ED. This is not possible unless A and B are the same point. But if A and B are the same point, they do not define the line AB. Please recheck your question.