Parallel Lines Assessment - Martinez, Teresa pd 4

In the picture above you will see that the GREEN lines, lines A and B, and parallel. This means that they can go on forever and never run into each other. Intersecting lines A and B is the PINK line, line C. This is the transversal. A transversal is a line that intersects two coplanar lines at two different points. One way we can prove that line A and line B are parallel is by using the 'Consecutive Interior Angles (Same-side Interior Angles) Theorem.' In this theorem we are just looking at the interior angles (<3,<4,<5, and <6). Basically if the two pairs of same-side interior angles (angles that lie in between the two parallel lines AND on the same side of the transversal) are supplementary, the you have proven the two lines are parallel.

In the picture above you will notice that the two lines running from left to right, labeled A and B, are parallel lines. This means they can run on forever and never run into each other. The line running up and down, intersecting them is line C. Line C is a transversal, a line that intersects two coplanar lines at two different points. One way we can prove that lines A and B are parallel is by using 'Converse of the Alternate Exterior Angles Theorem' which basically says that if two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel. A pair of alternate exterior angles (angles that lie on opposite sides of the transversal AND on the outside of the parallel lines) in this picture are <1 and <7. If the given to these angles were that angles 1 and 7 are both 120 degrees, then you would know that they are both equal, which makes them congruent. And if these angles are congruent then according to this theorem, lines A and B are parallel.

Teresa's line and angle project, 4th period.

Himalayas, found on the boarder of India.

Angle ACB and angle BCA are adjacent because they share ray CB

Angle ACB and angle BCD form a linear pair, because they share line ACD

Angle 123 is an obtuse angle because it measures more then 90 degrees.

The Great Wall of China, found in China.

Angle DY is a straight angle because it measures at 180 degrees.

Angle 123 is an acute angle because it measures less then 90 degrees.

Angle ABC is a right angle because it is exactly 90 degrees.

The Bank of China. A famous Hong Kong landmark.

Angle CBD and angle DBA are adjacent because they share ray BD

Angle CBD and angle DBA form a linear pair because they share line CBA

Angle 152 and angle 453 are vertical angles because they are formed by 2 non adjacent lines (153 and 452)
 that intersect eachother.

Angle 6 10 9 and angle 7 10 8 are vertical angles because they are formed by 2 non adjacent line (6 10 8 and  7 10 9) that intersect eachother.