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Transcript
Proving Lines Parallel Lesson 3-2 Geometry Additional Examples Use the diagram above. Which lines, if any, must be parallel if are supplementary? It is given that 3 and The diagram shows that 3 and 2 are supplementary. 4 and 2 are supplementary. Because supplements of the same angle are congruent (Congruent Supplements Theorem), 3 4. Because 3 and 4 are congruent corresponding angles, EC || DK by the Converse of the Corresponding Angles Postulate. 2 Proving Lines Parallel Lesson 3-2 Geometry Additional Examples Find the value of x for which || m. The labeled angles are alternate interior angles. If || m, the alternate interior angles are congruent, and their measures are equal. Write and solve the equation 5x – 66 = 14 + 3x. 5x – 66 = 14 + 3x 5x = 80 + 3x Add 66 to each side. 2x = 80 Subtract 3x from each side. x = 40 Divide each side by 2. Proving Lines Parallel Lesson 3-2 Additional Examples A rectangular wooden frame has a diagonal metal brace. The angles indicated were measured to be equal. Which sides are parallel? Explain. The top and bottom sides, or AB and CD, are parallel. By the Converse of the Alternate Interior Angles Theorem, the lines that contain and AB and CD are parallel. Geometry