2-6 Proving Angles Congruent
Objective
To prove and apply theorems about angles
Lesson Vocabulary
- theorem
- paragraph proof
In the Solve It, you may have noticed a relationship between vertical angles. You can prove that this relationship is always true using deductive reasoning. A theorem is a conjecture or statement that you prove true.
Essential Understanding You can use given information, definitions, properties, postulates, and previously proven theorems as reasons in a proof.
Take Note: Theorem 2-1 Vertical Angles Theorem
Vertical angles are congruent.
When you are writing a geometric proof, it may help to separate the theorem you want to prove into a hypothesis and conclusion. Another way to write the Vertical Angles Theorem is “If two angles are vertical, then they are congruent.” The hypothesis becomes the given statement, and the conclusion becomes what you want to prove. A two-column proof of the Vertical Angles Theorem follows.
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs