In conclusion, doing this for each one of the pairs of sides gives the required proof. Theorem 10: If two angles are supplementary to the same angle, or to equal angles, then they are equal to each other. Triangle Vocabulary, Supplementary Angles, Vertical Angles, Angle Sum. And, we'll use one of the other sides as the transversal line. In other words, the two opposing sides will be used as the parallel lines. So, let's apply the above theorem to each pair of sides. If the sum of the measures of two angles is 180, then the angles are supplementary. We have already proven that for the general case of parallel lines, a transversal line creates interior angles that sum up to 180°.īut, a parallelogram is simply two pairs of parallel lines. Therefore, it's a simple use of the properties of parallel lines to show that the consecutive angles are supplementary. You may also use the glossary to help you. Words to Know Fill in this table as you work through the lesson. Calculate unknown using complementary and supplementary angles. statements using complementary and supplementary angles. The definition of a parallelogram is that both pairs of opposing sides are parallel. Complementary and Supplementary Angles Identify and supplementary angles. 10 Dislike Share Save mroldridge 27.7K subscribers Supplementary Angles are ones that add up to a straight line, and that means they add to 180 degrees. Show that the pairs of consecutive angles are supplementary. Solution: We know that the sum of supplementary angles is 180. We'll prove this property using one of the theorems about parallel lines - the Consecutive Interior Angles Theorem. This property will be very useful in many problems involving parallelograms. Geometry Theorem 10.4: If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles. One of the basic properties of parallelograms is that any pair of consecutive angles are supplementary.
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