Alternate+Interior+Angles+Theorem+and+Alternate+Exterior+Angles+Theorem+,+4

Ⓐⓛⓣⓔⓡⓝⓐⓣⓔ Ⓘⓝⓣⓔⓡⓘⓞⓡ Ⓐⓝⓖⓛⓔⓢ Ⓣⓗⓔⓞⓡⓔⓜ ⓐⓝⓓ Ⓐⓛⓣⓔⓡⓝⓐⓣⓔ Ⓔⓧⓣⓔⓡⓘⓞⓡ Ⓐⓝⓖⓛⓔⓢ Ⓣⓗⓔⓞⓡⓔⓜ  By: Amanda Koch, Andie Drummond, Caroline Fiss and Sara Schwartz, Period 4





 **Proof.** Since //k// || //l//, by the [|Corresponding Angles Postulate] , 1 5. Therefore, by the definition of [|congruent angles] , //m//1 = //m//5. Since 1 and 2 form a [|linear pair], they are [|supplementary] , so //m//1 + //m//2 = 180°. Also, 5 and 8 are supplementary, so //m//5 + //m//8 = 180°. Substituting //m//1 for //m//5, we get //m//1 + //m//8 = 180°. Subtracting //m//1 from both sides, we have //m//8 //=// 180° − //m//1 = //m//2. Therefore, 2 8. You can prove that 3 5 using the same method.

If you are unable to see the picture, go to http://www.mathwords.com/a/alternate_interior_angles.htm. The two horizontal lines are parallel, which are the alternate interior angles? Which are alternate exterior angles?

Answer to 3 shown as 2. The value of x is 54. X is 54 because the measure of angle 8 is 112. The measure of angle 8 is 112 because angle 3 is congruent to angle 2 because of the vertical angle congruence theorem, and angle 2 is congruent to angle 7 because of the alternate interior angle's theorem, and the measure of angle 8 + the measure of angle 7 =180 degrees because they are a linear pair. Then you solve for x, (2x+4)=112. Because you know that the measure of angle 8 = 2x +4. Answer to 5, Alternate exteriors angles: angle 3 and angle 6, angle 4 and angle 5. Alternate Exterior: angle 2 and angle 7, angle 1 and angle 8. You can also solve this problem using the alternate exterior angles theorem, because angle 1 and angle 8 are alternate exterior angles, and angle 1 is 112 because it is supplementary to angle 3, then solve using the same equation, 2x+4=112, x=54. Very Helpful Websites!! [] http://hotmath.com/hotmath_help/topics/alternate-interior-angles-theorem.html []

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