410 likes | 559 Views
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. A RAY consists of a point on a line and all points on one side of the point. D. ●. This ray can be called AK or AD
E N D
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 A RAY consists of a point on a line and all points on one side of the point. D ● This ray can be called AK or AD The beginning of the name is the endpoint, A. K ● 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● T● RAY A RAY
ANGLES Oh, Mrs. C, you are tooooooo funny!
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 ● A DAE EAD n Side n E ● A Vertex Side
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 – 3 D – Huh? C A 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°
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. PQS = SQR ~ S P Q R
Definition Complementary angles are two angles that total 90 degrees 60º 30º and ___ 27º and ___ 12º and ___ 63º 78º
Definition Supplementary angles are two angles that total 180 degrees 155º • º and ___ • 67º and ___ • 124º and ___ 113º 56º
DEFINITION Straight angle is an angle that is the union of opposite rays. It makes a straight line and measures 180º
DEFINITION Linear anglesare 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)