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1.1 Angle Pair Relations straight angle an angle that is also a straight line, has a measure of 180o linear pair a pair of angles that make a line; 2 angles that are adjacent and supplementary adjacent angles 2 angles that share a common side or ray have a common vertex, and no interior points in common supplementary angles 2 angles whose measures have a sum of 180o 40o 140o *Note: All linear pairs are supplementary angles, but not all supplementary angles are linear pairs!! vertical angles 2 nonadjacent (opposite) angles formed by two intersecting lines interior angles angles formed on the inside of two lines cut by a transversal exterior angles angles formed on the outside of two lines cut by a transversal EXTERIOR INTERIOR EXTERIOR parallel two or more lines on a flat surface that do not intersect (no matter how far they extend) >> >> Arrowheads at the end of lines indicate that they extend indefinitely. Marks on pairs of lines or segments like > and >> indicate that the lines are parallel. perpendicular two lines or segments that meet (intersect) to form a 90o angle The small box at the point of intersection of two lines or segments indicates that they are perpendicular (form right angles) transversal a line that intersects two or more lines r and w are transversals Use what you know about straight angles and vertical angles to find the measures of missing angles b and d, f and k, and r and s. Label each angle with its measurement. Be prepared to explain your thinking. Compare the measures of angles a and d, and then compare the measures of angles b and e. Compare the measures of angles f and j, and then compare the measures of angles g and k. Compare the measures of angles t and r, and then compare the measures of angles n and s. corresponding angles a pair of angles that are in the same "corresponding" location relative to the parallel line and transversal . . . angles on the same side to their respective parallel line and on the same side of the transversal conjecture - (an inference based on incomplete evidence) If two parallel lines are cut by a transversal, then the corresponding angles are . . . Use what you know about straight angles, vertical angles, and what you learned from the previous example to find the measures of angles c, h and w. Compare the measures of angles c and d. Compare m<h and m<j. Compare m<w and m<s. alternate interior angles a pair of angles that are on the inside of the parallel lines and opposite sides of the transversal . . . conjecture - (an inference based on incomplete evidence) If two parallel lines are cut by a transversal, then the alternate interior angles are . . . Use all that you now know, lets make some more comparisons. Compare the measures of angles b and d. Compare m<g and m<j. Compare m<r and m<s. consecutive interior angles a pair of angles that are on the inside of the parallel lines and same side of the transversal . . . aka. same side interior angles conjecture - (an inference based on incomplete evidence) If two parallel lines are cut by a transversal, then the consecutive interior angles are . . . Classify each of the following pairs of angles as corresponding, alternate interior, same side interior, straight, or "none" of these. What conditions are necessary to be able to say that the pairs of corresponding angles or alternate interior angles are congruent? If m<2 = 670, what is m<5? If m<4 = 6x0 and ,<6 = 9x0, find the m<4. Explain your steps.