Special Angles Created With Parallel Lines

There are 4 types of special angles that can be made with parallel lines that are cut by a transversal. A transversal is a line that intersects two or more other coplanar lines. Shown in the image below:

When the transversal cuts between the two parallel lines it forms three types of angle pairs: Corresponding angles, Alternate interior angles and Alternate exterior angles.

Once the Parallel lines are cut by the transversal , the corresponding angles are always congruent , unless the two angles don't equal up to 180 degrees.

Since the corresponding angles angles are congruent, the alternate interior angles will be too.

The alternate exterior angles will also be congruent because the interior angles are already congruent and because they're verticle angles

Constructing Perpendicular bisectors

To find the perpendicular bisectors you need to have a compass. To find them you need to use your compass and set it to a specific length and draw an arc from two of the points, once they cross you connect the two points to form the perpendicular bisector for that line segment

 Watch the video below for further explanation.

http://www.mathopenref.com/constbisectline.html
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The Congruence shortcuts

There are 4 different congruence shortcuts, and you use them to find out whether two triangles are congruent or not. The types are: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS).

All three sides are marked with congruent marks
 stating that they're both congruent

SSS: If three sides of a triangle is congruent to three sides of another triangle then they are both congruent.








SAS: If two sides of a triangle and the included angle are congruent to the two sides of another triangle and its included angle then the two triangles are congruent

ASA: Triangles are congruent if any two angles and their included side are equal in both sides.









AAS: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both angles