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
Rotation matrix wikipedia , lookup
Technical drawing wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Perceived visual angle wikipedia , lookup
Integer triangle wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Multilateration wikipedia , lookup
Trigonometric functions wikipedia , lookup
4. Angles Angles 1. A whole turn Angles at a point add up to 360° 53° + 80° + 140° + 87° = 360° 2. A quarter of a turn Right angle = 90◦ 1 4. Angles 3. A straight line Angle on a straight line is equal to 180° 4. Acute Angles - The acute angle is the angle which is less than 90°. 2 4. Angles 5. Obtuse Angles Obtuse angles are larger than 90° but smaller than 180° Reflex Angles Angles larger than 180° (straight line) are called reflex angles. https://quizlet.com/87601233/flashcards 3 4. Angles Drawing angles This is a protractor; it helps you measure angles, in degrees: Example: Construct and angle of 50° Step 1: Draw a sketch 50◦ 4 4. Angles Step2: Draw a straight line Step 3: Put the centre of the protractor on the mark with the start line and use a protractor and measure an angle of 50° Step 3: Using a ruler draw a straight line. 5 4. Angles Step 4: Draw and arc and label the angle 50° http://www.mathsisfun.com/geometry/protractorusing.html 6 4. Angles Constructing Triangles s Constructing ∆ given 2 sides (cm) and 1 angles (°) Example: Construct ∆ ABC, AB = 6.5 cm, AC = 7.5 cm and Measure BC 1st step: Draw a sketch and label it. C A 50◦ B 6.5cm 2nd step: Draw a line of 6.5cm and name it AB A B 6.5cm 7 A=50°. 4. Angles 3rd step: Draw A=50° and line AC = 7.5cm C 7.5cm A 6.5cm B 4th Step: Draw line BC and measure BC C 7.5cm A B 6.5cm 8 4. Angles Constructing ∆s given 1 side (cm) and 2 angles (°) Construct ∆ XYZ, XY = 8cm, X = 52° and Y=64°. 1st step: Draw a sketch and label it. Z 52◦ X 64◦ 8cm Y 2nd step: Draw a line of 8 cm and name it XY X 3rd step: Draw 8cm Y X=52° X 8cm 9 Y 4. Angles 4th step: Draw Y=64° Z 52◦ X Z = 64◦ 64◦ 8cm Y Therefore, it is an isosceles triangle. 10 4. Angles Parallel lines Lines are parallel if they are always the same distance apart. They are called "equidistant", and will never meet. Non-Parallel lines 11 4. Angles Angle calculations Angles at a point add up to 360° Adjacent angles Angles on a straight line are called adjacent angles and add up to 180° Angles on a straight line add up to 180◦ 12 4. Angles Corresponding angles When two lines are crossed by another line (called the Transversal): Corresponding Angles are equal Alternate angles (Angles found in a Z-shaped figure) Angles are equal. 13 4. Angles Vertically opposite angles Angles a and c are equal and also d and b are equal and are called vertically opposite angles. https://quizlet.com/89005695/scatter https://quizlet.com/89006216/learn Example: Find angles a and b We can use the fact that angles around a point add up to 360° Therefore, angle a is 360° - 270° = 90° Angle a = 90° Angle b = 360° -180° - 30° = 150° Angle b = 150° 14 4. Angles Example: Given the diagram below, determine the values of the angles b, c, d, e, f, g and h. Give angle facts. Step 1: b = 180°-60°=120° (adj angles on a straight line) Step 2: b and c are equal. (vertically opposite angles). Therefore, c = b = 120° Step 3: d and 60° are equal (vertically opposite angles). Therefore, d = 60° Step 4: d and e are equal. (alternate angles). Therefore, e = d = 60° Step 5: b and f are equal (corresponding angles). Therefore, b = f=60° Step 6: g and f are equal ( vertically opposite angles). Therefore, g = f = 120° Step 7: h and d are equal (corresponding angles). Therefore, h = d = 60° 15