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What Are Linear Pair and Vertical Angles?

A pair of adjacent angles created when two lines intersect. Vertical Angles: The angles across from each other when two lines intersect.

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EXAMPLES OF LINEAR PAIR AND VERTICAL ANGLES

This example is a linear pair because 𝐴𝐶𝐷 is adjacent (across) of 𝐷𝐶𝐵 . Also, It is important to understand that these two pairs are supplementary (180°) if added together. This is often called as the LINEAR PAIR THEOREM. This image is an example of vertical angles because in order for <1 to equal <3, they have to be across from each other. This is the same with <2 equaling <4. This is called the VERTICAL ANGLE THEOREM. From precious learning of the linear pair, you should know that <1+<2= 180° because they are adjacent angles.

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HOW ARE LINEAR PAIR AND VERTICAL ANGLES USED IN REAL LIFE?

WHY ARE THEY IMPORTANT?

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LETS USE THIS MAP A B C D Let’s say we are trying to find the distance of A,B, and C. We know D equals half a mile and that A and D equals 1 mile and it is a straight street. Using the vertical theorem we know D = B, meaning B also equals ½ a mile. The pair of A and D is the Linear Pair Theorem because it equals a straight line or 180°. From using both the linear pair theorem and vertical theorem, we know all of the rest equals ½ mile also. This proves that we can use these theorems to find distance and so many other things.

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