​Standard

MGSE8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

TRANSVERSAL

a line that intersects two or more coplanar lines.

​

In the examples to the right,

the transversals are in red.

Parallel Lines and the angles created

We are going to focus on three kinds of angles created when a transversal crosses over parallel lines.

CORRESPONDING ANGLES

Angles in the same position on the top and on the bottom.

​

The two angles in the picture

are both in the UPPER RIGHT.

Four Pairs of Corresponding Angles

∠1 and ∠5 are corresponding

∠2 and ∠6 are corresponding

∠3 and ∠7 are corresponding

∠4 and ∠8 are corresponding

Corresponding Angles are EQUAL

ALTERNATE INTERIOR ANGLES

​Angles inside the two parallel lines and are on opposite sides of the transversal.

​

In the picture, the two blue angles are

Alternate Interior Angles.

Alternate Interior Angles are EQUAL

SAME SIDE INTERIOR ANGLES

​Angles inside the two parallel lines and are on the same side of the transversal. (other names: Consecutive Interior Angles (IXL))

​

In the picture, the two green angles are Same Side Interior Angles.

​Same Side Interior Angles are SUPPLEMENTARY (180°)