Lines and Angles Intro.

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Presentation transcript:

Lines and Angles Intro

Classify angles by size Classify angles by size Quick Review: Classify angles by size Classify angles by size Acute: 0<90 Right: 90 Obtuse: 90<180 Straight: 180

Intersecting Lines: Perpendicular Lines: Parallel Lines: Lines in a plane that intersect (or cross) Can cross at any angle Examples: Perpendicular Lines: Lines that intersect at a right angle (90°) Symbol for perpendicular Symbol for not perpendicular Parallel Lines: Lines in a plane that do not intersect (will never cross) Symbol for parallel lines is II Symbol for not parallel lines is II

Adjacent Angles: Vertical Angles: Linear Pair: Have a shared vertex and shared side (they are ‘next to’ each other or ‘touching’) Examples: Vertical Angles: Formed by intersecting lines, but are non-adjacent (they are ‘across the vertex’ from each other, don’t share a side) Vertical Angles are congruent (equal angle measure) Linear Pair: 2 adjacent angles that form a straight line (they make a straight line together) Straight Line = 180° = a linear pair

Supplementary Angles: Two angles whose sum is 180° Two angles who together form a straight angle/straight line (because a straight line is 180°) Examples: Complementary Angles: Two angles whose sum is 90° Two angles who together form a right angle (because a right angle is 90°) J K 130° 50° <J & <K are supplementary. 1 2 <1 and <2 are supplementary M J K O <JKO & <MKO are complimentary A B 40° 50° <A & <B are complementary.

*Tip: How to remember which is which? Think: "C" of Complementary stands for "Corner" Corner is a Right Angle "S" of Supplementary stands for "Straight" 180 degrees is a straight line

Find the Missing Angle Find the measure of <1 1 Solution: 63° Solution: Since <1 and the 63° angle are a linear pair (form a straight line together), they must add to 180°. If <1 is unknown, call it x. Write an equation to find the unknown angle. x + 63 = 180 -63 -63 x = 117 <1 = 117° x 63°

Find the Missing Angle Angle x and angle y are supplementary angles. If angle y is 3 times greater than the measure of x, what is the measure of each angle? x y Solution: Since <x and <y are supplementary, they must add to 180°. If <x is unknown, call it x. If <y is three times <x, then <y must be = 3x because it will be 3 times bigger. *tip- express all unknowns in terms of just one variable (not two) Write an equation to find the unknown angle. x + 3x = 180 4x = 180 4 4 x = 45 <x = 45° and <y = 135° x 3x