In today's lesson, we'll prove the Linear Pair Perpendicular Theorem: This theorem states that if two straight lines intersect at a point, and the linear pair of angles they form have an equal … [Read more...] about Linear Pair Perpendicular Theorem
Lines and Angles
What is a line?
A line is an abstract concept. It has no width, only length, and that length is infinite in both directions. One of the formal definitions of a line is that it is the collection of all points that are the same distance from two other points on a plane:
When 2 lines or line segments intersect, they form angles:
We measure angles in units called degrees, and marked with a °, where a full circle is 360°.
Now that we've briefly explained the basic concept of lines and angles in geometry, let's scroll down to the post below that explains these concepts more in depth. For specific geometry problems in the area of lines and angles, check out the following links:
Intersecting Lines and Angles
In today's lesson, we will prove the Converse of the Corresponding Angles Theorem. We will use the very useful technique of proof by contradiction. We had earlier said axiomatically, with no proof, … [Read more...] about Converse of the Corresponding Angles Theorem
In today's lesson, we will prove the alternate interior theorem, stating that interior alternating angles and exterior alternating angles between parallel lines are congruent. Prove: Interior … [Read more...] about Alternate Interior Angles Theorem
The Theorem The Consecutive Interior Angles Theorem states that the two interior angles formed by a transversal line intersecting two parallel lines are supplementary (i.e: they sum up to … [Read more...] about Consecutive Interior Angles Theorem
In today's lesson, we'll see a detailed step by step proof of the vertical angles theorem, which says that opposite angles of two intersecting lines are congruent. Plus, learn how to solve similar … [Read more...] about Vertical Angles Theorem
In today's lesson, we will see a step by step proof of the Perpendicular Transversal Theorem: if a line is perpendicular to 1 of 2 parallel lines, it's also perpendicular to the other. In the … [Read more...] about Perpendicular Transversal Theorem
In today's lesson, we will learn a step-by-step proof of the Converse Perpendicular Transversal Theorem: If two lines are perpendicular to a 3rd line, then they are parallel to each other. In the … [Read more...] about Converse Perpendicular Transversal Theorem