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Geometry

Geometry. The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids. Lines of Symmetry. A line that divides a figure into two halves that are reflections of each other. Transformations. Reflection. Rotation.

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Geometry

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  1. Geometry The mathematical study of the properties, measurements, and relationships of points, lines, planes, surfaces, angles, and solids.

  2. Lines of Symmetry • Aline that divides a figure into two halves that are reflections of each other.

  3. Transformations • Reflection • Rotation • Translation

  4. Two-Dimensional Figures

  5. Polygons • A simple closed figure formed by 3 or more sides. • The number of sides determines the name of the polygon.

  6. Regular Polygons • A regular polygon is a polygon with all sides congruent and all angles congruent.

  7. Triangles • A polygon with 3 sides and 3 angles. • Triangles can be classified by the length of their sides. • Triangles can be classified by the kind of angles.

  8. Triangles Classified by their sides • Equilateral Triangle • -all 3 sides equal in length • -all 3 angles equal in measure

  9. Triangles Classified by their sides • Isosceles Triangle • -2 sides are congruent • -the two angles opposite the congruent sides, angles K and L, are the base angles • -the base angles are congruent K L M

  10. Triangles Classified by their sides • Scalene Triangle • -0 sides equal in length

  11. Triangles Classified by their angles • Acute Triangle • -all 3 angles acute The sum of the angles in a triangle equals 180°. 60° 60° 60°

  12. Triangles Classified by their angles • Obtuse Triangle • -1 obtuse angle • -2 acute angles The sum of the angles in a triangle equals 180°. 25° 35° 120°

  13. Triangles Classified by their angles • Right Triangle • -1 right (90°) angle • -2 acute angles The sum of the angles in a triangle equals 180°. 60° 90° 30°

  14. Quadrilaterals • A polygon with 4 sides. • Some special quadrilaterals include: • Square • Rectangle • Parallelogram • Rhombus • Trapezoid

  15. Square • All sides equal in length • 4 right (90°) angles • Opposite sides parallel 90° 90° 90° 90° • The sum of the angles equals 360°. 90°+ 90° + 90° + 90° = 360° 90° x 4 = 360°

  16. Rectangle • Opposite sides equal in length • 4 right (90°) angles 90° 90° • Opposite sides parallel 90° 90° 90°+ 90° + 90° + 90° = 360° • The sum of the angles equals 360°. 90° x 4 = 360°

  17. Rhombus • All sides equal in length 100° 80° • Opposite sides parallel 80° 100° • The sum of the angles equals 360°. 80°+ 80° + 100° + 100° = 360°

  18. Parallelogram • Opposite sides parallel 100° 80° 80° 100° • The sum of the angles equals 360°. 80°+ 80° + 100° + 100° = 360°

  19. Trapezoid • Has one pair of parallel sides 80° 80° 100° 100° • The sum of the angles equal 360°. 80°+ 80° + 100° + 100° = 360°

  20. Compare a rectangle and a parallelogram. Are alike because: • four sides • opposite sides parallel • opposite sides congruent Are different because: • rectangles have four right angles

  21. Find the missing angle measurement in the quadrilateral. 100° 100° 80°  1 = ____ 80°  1

  22. Find the missing angle measurement in the triangle. 30°  1 = ____ 60°  1 90°

  23. Find the missing angle measurement in the quadrilateral. 100°  1 = ____ 90° 80° 90°  1

  24. Find the missing angle measurement in the triangle.  1 24°  1 = ____ 78° 78°

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