2ND SEMESTER!!!!!

Blog assignment: Characteristics of angles

An angle is typically classified into four categories including acute, right, obtuse, and straight. An acute angle is one which has a degree measurement greater than 0° but less than 90°. A right angle has a 90° angle measurement. An obtuse angle has a measurement greater than 90° but less than 180°, and a straight angle, which looks like a straight line, has a 180° angle measurement.

Two angles are known as congruent angles if they have the same measurement. If their sum is 90°, then they are said to be complementary angles. If their sum is 180°, they are supplementary angles. Angles can be bisected (divided in half) or trisected (divided in thirds) by rays protruding from the vertex.

When two lines intersect, they form four angles. The angles directly across from each other are known as vertical angles and are congruent. The neighboring angles are called adjacent because they share a common side. If the lines intersect such that each angle measures 90°, the lines are then considered perpendiculair or orthogonal.

In addition to size, angles also have trigonometric values associated with them such as sine, cosine, and tangent. These values relate the size of an angle to a given length of its sides. These values are particularly important in areas such as navigation, astronomy, and architecture.

FOTO'S:

-Acute

-Right

-Obtuse

-Straight

classwork 10/29/2013

    Points: A point is a dot that is so small that its height and width are actually zero!

    Lines: A line is as wide as a point, infinitely thin, having an infinite number of points, (in a straight row), extending forever in both the directions.

    Angles: An angle (∠) is made up of a vertex (a point), two arms (rays), and an arc. They are arranged so that the endpoint of the arms are the same as the vertex, and the arc runs from one arm to another. The size of an angle depends on how big the arms are opened, and they are measured in degrees.

    Solids: Solids are shapes that you can actually touch. They have three dimensions, which means that the have length, width and height.

    Measurements: When measuring length, simply put get a ruler and place the '0' on the endpoint of the segment you wish to measure. Then move the ruler so that the edge of the ruler fits the line exactly. Read the marking on the ruler on the other endpoint. That is the length of the ruler.

    Parallel lines: Parallel lines are straight lines that never intersect, which means that they never cross. Notice that when we look at parallel parts of shapes there is no place where they intersect even if we extend the lines.

    Symmetry: A figure is considered to have reflectional symmetry when a half of the figure coincides with the other half when folded in half (an easier way to say it would be saying it looks exactly the same on both sides).

    Transformation: Transformation is when we change the size, orientation, and/or position of a shape. Note that transformation is usually done on graph paper to avoid excessive meaurements and ensure accuracy.

    Coordinates: Coordinates are very useful in daily lives. Without them, the longitude and latitudes, and grid references would be lost, making it impossible to navigate. Many of the things you learn in computer literacy lessons, such as image editing, would be harder.

Plane shapes: Any shape that can be drawn in the plane is called a plane figure.

Ex:

1) Triangle: A triangle is a shape with three sides. It can be classified according to its sides or angles, with three kinds each. Here they are:

-          Equilateral triangles, which are also equiangular triangles, have three sides equal and three angles equal. Their angles are always 60°.

-          Isosceles triangles are triangles in which two of the sides are equal. The non-included angles of the sides are also equal.

-          Scalene triangles have no equivalence in any way.

-          Right triangles are triangles with a right angle. The longest side of such triangles is called a hypotenuse.

-          Obtuse triangles are triangles with an obtuse angle.

-          Acute triangles are triangles with no right or obtuse angle.

2) Quadrilaterals: A quadrilateral is a shape with four sides. You will spend a lot of time with these. They can be classified into many different categories:

  - Parallelograms are shapes where opposite sides and angles are equal. The opposite sides are parallel, hence the name.

        -Rectangles are parallelograms where the angles are all 90°. Its width or breadth refers to the shorter sides, while its length refers to its longer ones.

      -  Rhombuses are parallelograms where all the sides are equal, and opposite angles are equal.

        -Squares are parallelograms that are both rectangles and rhombuses, i.e. all angles are right and all sides are equal.

    -Trapeziums, called trapezoids in American English, have two opposite sides that are parallel. The parallel sides are sometimes called the upper and lower bases.

       - Right-angles trapeziums are trapeziums with a right angle.

        -Isosceles trapeziums are trapeziums where the laterals sides are equal but not parallel.

        -Scalene trapeziums are trapeziums that fall into neither category.

Other:

·         Pentagons have five sides.

·         Hexagons have six sides.

·         Heptagons or septagons have seven sides.

·         Octagons have eight sides.

·         Nonagons have nine sides.

·         Decagons have ten sides.

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