* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Angles
Survey
Document related concepts
Rotation formalisms in three dimensions wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Technical drawing wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
Lesson 5.1 – Measuring and Drawing Angles Drawing Angles 1. Construct a ray and label the vertex 2. Place protractor guide over the vertex 3. Starting at zero side, find the point for the measurement 4. Mark the point and draw another ray going through it Angles: Ray – begins with and endpoint and extends infinitely in one direction Angle – formed by two rays with a common endpoint Vertex – the endpoint of an angle Naming Angles: Angle symbol and a letter or number Angle symbol and the vertex label Angle symbol and three letters (point on ray, vertex, point on other ray) ____________ __________ __________ Angle Types: Acute – greater than 0° degrees and less than 90° Right – exactly 90°, or a square corner Obtuse - greater than 90° degrees and less than 180° Straight - exactly 180°, or a line Reflex – greater than 180° degrees and less than 360° _____________ Lesson 5.2 – Reasoning with Angle Measures Angles Supplementary Angles – two or more angles that equal 180° Complementary Angles – two or more angles that equal 90° Adjacent Angles – angles sharing a common side (vertex, ray) Vertical (Opposite) Angles – congruent angles formed where 2 lines intersect Angle Reasoning Rules Triangle – sum of angles equals 180° Parallelogram – sum of angle measurements equals 360° Polygons – count how many triangles are in it and multiply by 180° Opposite angles – congruent to one another Perpendicular Lines create 4 right angles Lesson 5.9 – Parallel Lines, Angle Relationships Parallel Lines – lines that never meet; always the same distance apart Transversal – line that crosses over parallel lines adjacent angles are supplementary, or total 180° Two pairs of vertical angles at each intersection Corresponding angles – created when angle measurements “slide” on transversal Lesson 5.10 – Parallelograms Parallelogram Formed by two pairs of parallel lines Terms Consecutive Angles – pairs of angles next to one another in parallelograms Opposite Interior Angles – angles in opposite corners of parallelogram Opposite Sides – sides formed by parallel lines Parallelogram Properties Opposite side pairs are parallel Opposite sides are congruent (same length) Opposite Interior angles are congruent (same degree measure) The sum of consecutive angle pairs is 180°