Transcript 1-5
1-5 Angle Relationships What are: adjacent angles linear pairs vertical angles complementary angles supplementary angles perpendicular lines Adjacent angles Adjacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points. 1 2 Linear Pair A linear pair is a pair of adjacent angles with noncommon sides that are opposite rays. 1 2 Definition Two angles, ABD and DBC, form a linear pair if and only if A, B, and C are collinear and D is not on AC . D A B C Name all the linear pairs JKF and FKG FKG and GKH F G K H J HKJ and JKF GKH and HKJ Vertical Angles Two angles are vertical angles if and only if their sides form two pairs of opposite rays. OR…When two lines intersect, they form two pairs of vertical angles. 2 1 3 4 Definition Complementary angles are two angles whose measures add up to 90° A C B D ABC CBD ABD 90 Try it Find the measures of 1, 2, 3. 2 1 3 134° m1 46 m3 46 m2 134 Definition Supplementary angles are two angles whose measures add up to 180° T R S U RST TSU 180 Linear Pair Postulate The angles in a linear pair are supplementary What is the difference? Supplementary because it adds to 180° Supplementary because it adds to 180° AND Linear pair because both angles are on the same line. Complementary or Supplementary? 41° 49° P R 41° 139° P S R is complement ary to P S is supplement ary to P Angles can be complementary or supplementary regardless of their location. If mX 64 find the measures of the angles that are complementary and supplementary to X Complementary Supplementary 90°− 64° = 26° 180°− 64° = 116° Review p. 46 Review p. 47 Assignment 1-5 Page 51, 8-17, 19-21 Angle Relationships Day 2 What are perpendicular lines? What can be assumed or not assumed in a drawing? Perpendicular Lines Lines, line segments or rays that form right angles are perpendicular. B A D C B Perpendicular Lines A C D Perpendicular lines intersect to form four right angles. Perpendicular lines intersect to form congruent adjacent angles. Segments and rays can be perpendicular to lines or other line segments and rays. The right angle symbol in the figure indicated that the lines are perpendicular. To Assume or Not to Assume… In the figure, do you think you would be justified in assuming that: B, C, and E are collinear? ACB FCE ? F A B E C BE ll GD? G D Make a List… Make a list of rules about what you think you can and cannot assume. F A B E C G What can and cannot be assumed You May Assume: Things that look straight are straight. You May Not Assume (unless marked): Points shown on a line are collinear. Exact measurements and relative sizes of figures. All points shown are coplanar. Parallel or perpendicular lines. Relative position of points are accurate (intersection, between-ness). Congruence To Assume or Not to Assume… Point S is between R and T. Points R,S, and T are collinear. RS ST Point S is the midpoint of RT. VR ZW ZYV is a right angle. VY<TY Z V Y W R S T Assignment 1-5 Day 2 Worksheet 1-5