objective: students will identify and use special pairs of angles and perpendicular lines

11

Upload: merry-sanders

Post on 01-Jan-2016

216 views

Category:

Documents


0 download

TRANSCRIPT

Objective:Students will identify and use special pairs of

angles and perpendicular lines.

Adjacent angles are two angles that lie in the same plane, have a common vertex, and a common side, but no common interior point.

1 2

3 4

Vertical angles are two nonadjacent angles formed by two intersecting lines

Vertical angles are ALWAYS congruent

12

34

Angles 1 and 3 are vertical;Angles 2 and 4 are vertical.

A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.

Linear pairs have a sum of 180 degrees.

12

Angles 1 and 2 form a linear pair

Complementary angles are 2 angles whose measures have a sum of 90 degrees

Complementary angles can be adjacent or nonadjacent

200

700

Supplementary angles are 2 angles whose measures have a sum of 180 degrees.

Supplementary angles can be adjacent or nonadjacent.

520 1280

Perpendicular lines intersect to form 4 right angles

Perpendicular lines intersect to form congruent adjacent angles

Segments and rays can be perpendicular to lines or other segments and rays

The right angle symbol in the figure indicates the lines are perpendicular

Lines p and q intersect to form adjacent angles 1 and 2. If m<1 = -3x+18 and m<2 = 8y-70, find the values of x and y so that p is perpendicular to q.

The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 and 2 form a linear pair, what are their measures?

X = -24, y = 20

37, 143

If m<A = 75, what are the complement and supplement of <A?

m<B = x. Name the complement and supplement of <B.

The supplement of an angle is twice the measure of the angle. Find the angle and its supplement.

The difference between the measures of 2 supplementary angles is 42 degrees. Find the angles.

A supplement of an angle is 6 times as large as the complement of the same angle. Find the angles.

C = 15, S = 105

C = 90-x, S = 180-x

60, 120

69, 111

72, C = 18, S = 108