ESSENTIALS OF GEOMETRY Rays and Angles Ch 1
- Slides: 40
ESSENTIALS OF GEOMETRY Rays and Angles Ch. 1. 5 and 1. 6 C. N. Colón Geometry St. Barnabas HS Bronx, NY
DEFINITION OF A RAY consists of a point on a line and all points on one side of the point. D● K● A This ray can be called AK or AD The beginning of the name is the endpoint, A.
DEFINITION OF OPPOSITE RAYS Opposite rays are two rays of the same line with a common endpoint and no other points in common C ● RAY A RAY T●
ANGLES Oh, Mrs. C, you are tooooooo funny!
This gle n a n is a
DEFINITION OF AN ANGLE An angle is a set of points that is the union of two rays having the same endpoint There are several ways to name this angle: D ● Sid e A DAE EAD Vertex A n Side E ● n
DEFINITION OF AN ANGLE In this case there is no confusion you name an angle by the vertex. A A
BIG ANGLE VS. LITTLE ANGLE obtuse angle acute angle
Angle B How many angles do you see? A– 1 B– 2 C C– 3 A D – Huh? D
DEFINITION OF DEGREE Degrees were developed by the Babylonians thousands of years ago. They divided a circle into 360 parts and called each part one degree.
Notation for angle measurement The symbol for degrees, as you probably already know, is a small superscript circle. 45° 37° 112°
WHAT IS A PROTRACTOR?
MEASURING AN ANGLE This is an acute angle and it measures 61º
MEASURING AN ANGLE This is an obtuse angle and it measures 127º
The measure of angle BVA is: A: 180 B: 125 C: 50 D: 25
ANGLE CONGRUENCE Angles are congruent if they have the same measure. A B
ANGLE ADDITION POSTULATE If point S is in the interior (middle) of angle PQR, then the measure of PQS + measure of SQR = measure of PQR S P Q R
BISECTOR OF AN ANGLE The bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent angles. Q ~ S P PQS = R SQR
Definition Complementary angles are two angles that total 90 degrees 60º 30º and ___ 63º 27º and ___ 78º 12º and ___
Definition Supplementary angles are two angles that total 180 degrees 25º and 155º ___ 113º 67º and ___ 56º 124º and ___
Angle 28º 49º 67º 100º 147º Complement Supplement
Angle Complement 28º 62º 49º 67º 100º 147 Supplement
Angle Complement Supplement 28º 62º 152º 49º 67º 100º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 67º 100º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 100º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 100º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 113º 100º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 113º 100º none 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 113º 100º none 80º 147º
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 113º 100º none 80º 147º none
Angle Complement Supplement 28º 62º 152º 49º 41º 131º 67º 23º 113º 100º none 80º 147º none 33º
DEFINITION Straight angle is an angle that is the union of opposite rays. It makes a straight line and measures 180º
DEFINITION Linear angles are two angles that share a side and make a line. We also called them supplementary angles Linear angles total 180°
DEFINITION Right angles are angles that measure 90°
DEFINITION Acute angles measure less than 90°
DEFINITION Obtuse angles are angles that measure more than 90° but less than 180°
DEFINITION Perpendicular lines are lines that intersect to form right angles. The shortest distance from any point to a line is the length of the perpendicular from the point to the line.
Definition A reflex angle is an angle that measures more than 180°
ASSIGNMENT p. 18 # 3, 4 p. 21 #4 -24 (e)
