Clil.geometry presentation-
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This document defines and describes various geometric shapes and concepts. It defines points, lines, line segments, rays, angles, parallel lines, triangles, quadrilaterals such as parallelograms, rectangles, squares, trapezoids, and rhombi. It also covers circles, areas, volumes, and properties of angles, triangles, parallelograms and polygons. Key concepts include classifying angles as acute, obtuse, right or straight, and properties of parallel lines, perpendicular lines, complementary and supplementary angles.
Clil.geometry presentation-
- 1. Geometry Concepts Point Line Ray Line segment Ray Angles Parallel Lines Triangles Quadrilaterals Parallelograms Area Circles Volume
- 2. A point can be described as a location in space. Represented by a dot and is named by writing a capital letter next to the dot. POINT
- 3. A line is a straight row of points that goes on forever in both directions. A line is drawn by using arrow heads at both ends. LINE
- 4. A line segment is a piece of a line that has two endpoints. A line segment is named for its endpoints. The segment with endpoints A and B shown to the right is named: LINE SEGMENT
- 5. A ray is a part of a line that has only one endpoint and goes on forever in one direction. A ray is named by using the endpoint and some other point on the ray: RAY
- 6. Lines that are on the same plane, but that never intersect (cross). PARALLEL LINES
- 7. Lines that intersect (cross). INTERSECTING LINES
- 8. Types of Angles • Classification – Acute angle: all angles are less than 90° – Obtuse angle: one angle is greater than 90° – Right angle: has one angle equal to 90° • Complementary angle: the sum of two angles is 90° • Supplementary angle: the sum of two angles is 180° • Adjacent angle: angles that share a side
- 9. An angle is made up of two rays that start at a common endpoint. The common endpoint is called the vertex. Named: ANGLE
- 10. Angles can be measured in degrees. The symbol for degrees is a small raised circle ° DEGREES
- 11. An angle of 180° is called a straight angle. When two rays go in opposite directions and form a straight line, then the rays form a straight angle STRAIGHT ANGLE
- 12. An angle of 90° is called a right angle. The rays of a right angle form one corner of a square. So, to show that an angle is a right angle, we draw a small square at the vertex. RIGHT ANGLE
- 13. Acute angles measure less than 90° ACUTE ANGLE
- 14. An Obtuse angle measures more than 90° but less than 180° OBTUSE ANGLE
- 15. Two lines are called perpendicular lines if they intersect to form a right angle. PERPENDICULAR LINES
- 16. Two angles are called complementary angles if the sum of their measures is 90°. If two angles are complementary , each angle is the complement of the other. COMPLEMENTARY ANGLES
- 17. Two angles are called supplementary angles if the sum of their measures is 180° SUPPLEMENTARY ANGLES
- 18. Triangles • The sum of the angles in a triangle is 180° • a – b < third side < a + b • The sum of the two remote interior angles is equal to the exterior angles • Types: Scalene Isosceles Equilateral Right No sides Two All One are equal sides are equal sides are equal Right angle
- 19. Polygons • The sum of the interior angles: (n - 2)(180°) • Classified by number of sides (n) – Triangle (3) – Quadrilateral (4) – Pentagon (5) – Hexagon (6) – Heptagon (7) – Octagon (8) – Nonagon (9) – Decagon (10) • Regular Polygon: all sides are congruent
- 20. Quadrilaterals PARALLELOGRAM TRAPEZOIDS Both pairs of opposite Only one pair of sides are parallel Opposite sides parallel RECTANGLE ROMBUS 4 equal sides ISOSCLES 4 right angles TRAPEZOID A trapezoid that has two equal sides SQUARE Both a rhombus and a rectangle
- 21. Properties of Parallelograms Diagonals bisect each other Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Consecutive angles are supplementary Diagonals form two congruent triangles Diagonals are perpendicular to each other Diagonals are Diagonals congruent to each other bisect their angles Diagonals are perpendicular to each other Diagonals bisect their angles
- 22. Circles Circumference A = πr2 C = 2πr or C = πd • Exact: express in terms of π • Approximate: use an approximation of π (3.14)