Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Line (geometry) wikipedia , lookup
Integer triangle wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Perceived visual angle wikipedia , lookup
Geometry Terms Point Line segment A location End Point A straight path between the points, called its endpoints. Line A straight path that goes on forever in both directions. Ray A straight path that goes on forever in one direction from an endpoint. Angles In Daily Life If we look around us, we will see angles everywhere. Review Naming an Angle To name an angle, we name any point on one ray, then the vertex, and then any point on the other ray. A B C For example: ABC or CBA We may also name this angle only by the single letter of the vertex, for example B. Review Types f Angles There are four main types of angles. Right angle Acute angle A B Obtuse angle A A C B B C Straight angle A B C C Right angle: An angle whose measure is 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle Examples Of Right Angle Examples Of Obtuse Angle Acute angle: An angle whose measure is less than 90 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle Examples Of Acute Angle Straight angle: An angle whose measure is 180 degrees. Straight Angle Right Angle Acute Angle Obtuse Angle Examples Of Straight Angle Lines in a plane What can you say about these pairs of lines? These lines cross, or intersect. These lines do not intersect. They are parallel. Angles Angles are measured in degrees. A quarter turn measures 90°. 90° It is called a right angle. We label a right angle with a small square called a square corner. Angles A half turn measures 180°. 180° This is a straight angle Angles 360° A full turn measures 360°. Adjacent Angles Two angles that have a common vertex and a common ray are called adjacent angles. “SIDE BY SIDE” A A C D Common ray B D B Common vertex E C F Adjacent ABD and DBC ABC and Angles DEF arenot adjacent angles Adjacent angles do not overlap each other. More examples of adjacent angles. 80º 45º 35º 55º 130º 85º 20º 50º Missing Angles Our learning objectives today •To calculate missing angles on a straight line, around a point and in a triangle. What do you need to know? Angles in a triangle add up to................. 180° Angles on a straight line add up to....... 180° Angles around a point add up to............. 360° Complementary Angles Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees. Example: These two angles are complementary. These two angles can be “put" together to form a right angle which is complementary! Supplementary Angles Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees. Example: These two angles are supplementary. These two angles can be “put" together to form a straight line! Find the missing angle. You do not have a protractor. Use the clues in the pictures. 1. x 55 X=35 Find the missing angle. You do not have a protractor. Use the clues in the pictures. 2. x 165 X=15 Calculate the missing straight line angle 69° 111° Calculate the missing triangle angle 89° 37° 54° Calculate the missing straight line angle 103° 35° 42°