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![]() With the definitions and axioms presented so far, we can now start deriving our first theorem, using our first formal proof – proving that the opposite angles of two intersecting lines are congruent. The angle addition postulate says that when two angles have a common vertex and common side, the measures of the smaller two angles added together is equal to. We say two angles are congruent if they have the same measure of their angle, in degrees. When two lines intersect and form 4 angles at the intersection, the two angles that are opposite each other are called “opposite angles” or “vertical angles” and these vertical angles are “congruent” – meaning they have the same shape and size. In other words, the measure of the larger angle is the sum of the measures of the two interior angles that make up the larger one. The angle addition postulate states that if a point, P, lies inside an angle B then m ∠ A B P + m ∠ P B C = m ∠ A B C We also commonly describe angles using the 3 points that define them, e.g: ∠ABC, where B is the vertex and BA and BC are the two rays that emanate from point B outward: We describe angles using this notation: ∠1 or ∠α, and their measure in degrees as m∠1 or m∠α. #ANGLES ADDITION POSTULATE DEFINITION GEOMETRY HOW TO#Prerequisites: Students should already know how to solve multi-step equations. ![]() It also includes solving problems using an angle bisector. We know that when we rotate enough to make half a circle we will have a straight line because of symmetry – we could have rotated the line in either direction, and the half-way point would be the same. This product provides a notetaking guide for students to use the Angle Addition Postulate to solve for missing angles and/or to set up and solve equations involving angles. So when we rotate enough to make half a circle (to point B3), the measure is 180°. #ANGLES ADDITION POSTULATE DEFINITION GEOMETRY FULL#When we complete a full circle, the measure of the angle is 360°, because as we said above, that is what a full circle measures. The angle formed between the original segment (AB0) and the subsequent positions (AB1, AB2…) keeps growing. Why? Let’s take a line segment (AB), and start rotating it around one of its end-points: We call the 2 angles that are next to each other and which form a straight line a "linear pair", or “supplementary angles”, and their sum is 180°. ![]()
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