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Geometry

Geometry. Angles . Angles describe the shape made by two straight lines that meet at a point Vertex –the point at which two lines meet Degrees are used to measure an angle Protractors are used to measure the number of degrees in an angle. Types of Angles. Acute angle

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Geometry

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  1. Geometry

  2. Angles • Angles describe the shape made by two straight lines that meet at a point • Vertex –the point at which two lines meet • Degrees are used to measure an angle • Protractors are used to measure the number of degrees in an angle

  3. Types of Angles • Acute angle • An angle that measures between 0 and 90 • Right angle • An angle that measures exactly 90 degrees • Obtuse • An angle that measures between 90 and 180 degrees • Straight • An angle that measures exactly 180 degrees

  4. Identify the type of angle

  5. Shapes and angles

  6. Types of Quadrilaterals

  7. Types of Triangles

  8. Circles • Perimeter is called Circumference • Diameter • Length of the line that goes from one edge, through the center, to the other edge of a circle • Radius • Length of any line that goes from the center of a circle to the edge • Pi (π) • The ratio of the circumference to the diameter

  9. Circle Formulas • Circumference • Pi * diameter (or pi * 2 * radius) • Area • Pi * radius * radius (pi r^2)

  10. Other area formulas • Triangle • ½ base * height • Square/Rectangle • Length * width • Don’t forget your units!!! When we calculate area, it is measured in SQUARE UNITS (sq ft, sq meters, sq in, sq cm, etc)

  11. Test your skill • Find the area and perimeter of the following 4m 5ft 0.5 m 4ft 6ft 14 cm

  12. Stretch Break • You have 3 ½ minutes

  13. Volume • Recall: area is measuring two dimensions, length and width. For volume, we measure three dimensions: length, width and height • When we calculated area, we multiplied the two dimensions together. So for volume, we will multiply three dimensions together • Don’t forget your units!!! When we calculate volume, it is measured in CUBIC UNITS (cu ft, cu meters, cu in, cu cm, etc)

  14. Volume formulas • Rectangular prism (a box of various shapes) • L * w *h • In general, area of base * height • (for rectangle box l * w is area of base) • We use this formula for shapes that are not so neat, like cylinders and triangular prisms (triangular boxes)

  15. Test your skill--volume

  16. Conversions in multiple dimensions • When converting units in multiple dimensions (ie more than one, ie area and volume) we must convert for each dimension • 1 cu ft = 1ft *1ft*1ft • =12 in*12in*12in=______ • 1cu m= 1m*1m*1m • =100cm*100cm*100cm=______

  17. Test your skill conversion • 3cu ft = _____cu in • 200,000 cu cm=_____cu m • 512 cu ft = _____cu yards

  18. Pythagorean Theorem • a^2+b^2=c^2 • Used in right triangles as a relationship between sides c b a

  19. Test your skill

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