![]() The Segment Addition Postulate is similar to the angle addition postulate, but you are working with line segments instead of adjacent angles. Angle Addition Postulate: The sum of the measure of two adjacent angles is equal to the measure of the angle formed by the non-common sides of the two adjacent angles. These cables placed at specific angles support the bridge’s structure by sharing the weight of the bridge evenly across its supports. Some bridges have cables connected to bridges at angles from the bridge floor to towers. ![]() The Howe truss is made up of two 60° triangles and the Fink truss is made with three 40° triangles. It is important the angles in each triangle are measured correctly, as roof trusses provide support for a roof. ![]() Roof trusses are beams of timber organized in triangles in the roofs of buildings. There are many applications of the postulate, especially in architecture and engineering. A and B are complementary, and C and B are complementary. Now you know how the postulate works, you must know how it can be used in real life. The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm. Theorem 8.3: If two angles are complementary to the same angle, then these two angles are congruent. Real-Life Application: Angle Addition Postulate The Angle Addition Postulate is that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two. You can find their resulting angle as the sum of 90° and 30° so ∠JKM is 120°. The angle ∠JKL is a right angle so it is 90°, and from the diagram, you will see LKM is 30°. Now you know how the postulate works, let’s work through an example and calculate the resulting angle.Īs you can see these angles share the same side KL, so they are adjacent. ![]() It is so full of definitions and examples. However- notice how the resulting angle changes? This is because it is the sum of the two adjacent angles. I am in LOVE with this flipbook that I made for the Protractor Postulate and Angle Addition Postulate in Geometry. You will find that changing points A, D, or C will affect the resulting angle it makes, without affecting the adjacent angle. Here’s a fun tool to play around with and explore how changing the size of two adjacent angles affects the measure of the resulting angle. ![]()
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