Parallel and Intersecting Lines
Two lines are parallel if one can be mapped onto the other with a translation.
Two lines are perpendicular if one can be mapped onto the other with a 90 degree rotation.
Two lines are perpendicular if one can be mapped onto the other with a 90 degree rotation.
Transversal
Classifying Angles
Complementary: two angles are complementary if and only if the sum of their measures is 90 degrees. In the image to the left, angle BOC and angle COD are complementary.
Supplementary: two angles are supplementary if and only if the sum of their measures is 180 degrees. In the image, angle AOB and angle BOD are supplementary. Adjacent angles: two angles are adjacent if and only if they're coplanar and share a vertex and a side. In the image, angle COD and angle DOE are adjacent. Perpendicular pair: two adjacent angles that are complementary. Angle AOB and angle BOD are a perpendicular pair. Linear pair: two adjacent angles that are supplementary. Angle AOE and angle DOE are form a linear pair. Vertical angles: non adjacent pair of angles formed by two intersecting lines. Angle DOE and angle AOC are vertical angles. |
Linear Pair Theorem:
Proof of Vertical Angles Theorem:
Corresponding Angles
•In the picture to the left, the blue angles are all corresponding
•Corresponding Angles Postulate: If there are corresponding angles, formed by a transversal across 2 parallel lines, then those angles are congruent
•Corresponding Angles Postulate: If there are corresponding angles, formed by a transversal across 2 parallel lines, then those angles are congruent
Proof of Same Side Interior Angles Theorem
Proof of Same Side Exterior Angles Theorem
Proof of Alternate Interior Angles Theorem
Proof of Alternate Exterior Angles Theorem
Converse Proof
We can use our knowledge about converse to switch information around and prove other things, like...
In this picture, I'm proving that two lines are parallel by using the converse of the same side interior angles proof (shown above)
You can also use a converse of Same Side Exterior Angles Proof, Converse of Alternate Interior Angles Proof, and Converse of Alternate Exterior Angles Proof
CONSTRUCTIONS
These are some constructions we learned in this unit, and I included the links (you have to copy and paste them) that I used to learn them so you can see how to construct them (you'll need a compass, ruler, and pencil).
- Construct a Right Angle (top left box) https://www.youtube.com/watch?v=n5wb7fitJGU&feature=youtu.be
- Construct Parallel lines using Congruent Corresponding Angles (left right box) https://www.youtube.com/watch?v=n5wb7fitJGU&feature=youtu.be
- Construct Parallel lines using Congruent Alternate Interior Angles (right bottom box) https://www.youtube.com/watch?v=n5wb7fitJGU&feature=youtu.be
- Construct Parallel lines using Perpendicular to Perpendicular (left bottom box) https://www.youtube.com/watch?v=n5wb7fitJGU&feature=youtu.be
More constructions:
-Construct perpendicular lines through a specific point OFF the line (top left box) https://www.youtube.com/watch?v=n5wb7fitJGU&feature=youtu.be
-Construct perpendicular lines through a specific point ON the line (top right box) https://www.youtube.com/watch?v=yI1DxgHZq6E&feature=youtu.be
-Construct a rectangle that is NOT a square (bottom right box) https://www.youtube.com/watch?v=Ng-B05qw9j0&feature=youtu.be
-Construct a square-two ways (bottom left box) https://www.youtube.com/watch?v=ADAj0oX28s4&feature=youtu.be