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Geometry (Revision Notes) - Coggle Diagram

- - - - Acute Angles lie between 0 degrees and 90 degrees
    - - Are angles that are exactly 90 degrees
    - - lie between 90 degrees and 180 degrees
    - - lie between 180 degrees and 360 degrees
  - - - An acute-angle triangle has all of its angles less than 90 degrees
    - - An obtuse-angle triangle has all of its angles less than 90 degrees
    - - An Isosceles Triangle has two of its sides equal length, and the angles opposite the equal sides are equal
    - - Has all 3 sides are equal to each other and all 3 angles are equal to each other
    - - All the sides and angles are not equal to each other
    - - If the angles of two triangles are the same, then their corresponding sides will also be in proportion to each other. When this is the case, the triangles are said to be equal to each other
  - - - Center
        
        The fixed point within the circle from which all points on the circle's circumference are equidistant.
      - Circumference
        
        The outer boundary or perimeter of the circle. It is the distance around the circle.
      - Radius
        
        The distance from the center of the circle to any point on the circumference. All radii of a circle are of the same length
      - Diameter
        
        The longest chord (a line segment with both endpoints on the circle) that passes through the center of the circle, connecting two points on the circumference. The diameter is twice the length of the radius.
      - Chord
        
        A line segment with both endpoints on the circle.
      - Tangent
        
        A straight line that touches the circle at only one point, known as the point of tangency.
      - Arc
        
        A part of the circumference of the circle. Arcs are named according to the two endpoints of the arc and the center of the circle. For example, "arc AB" or "arc ACB."
      - Sector
        
        A region bounded by two radii and an arc of the circle.
    - - The region between the circle and a chord.
  - - - Parallelogram
        
        Opposite sides are parallel.
        
        Opposite sides are equal in length.
        
        Opposite angles are equal.
        
        Consecutive angles are supplementary (their sum is 180 degrees).
        
        Diagonals bisect each other (they intersect at their midpoint).
      - Rectangle
        
        All properties of a parallelogram apply.
        
        All angles are right angles (90 degrees).
        
        Diagonals are equal in length.
      - Square
        
        All properties of a parallelogram and rectangle apply.
        
        All sides are equal in length.
        
        All angles are right angles (90 degrees).
        
        Diagonals are equal in length and bisect each other at right angles.
      - Rhombus
        
        All properties of a parallelogram apply.
        
        All sides are equal in length.
        
        Opposite angles are equal.
        
        Diagonals bisect each other at right angles
      - Trapezium
        
        At least one pair of opposite sides is parallel.
        
        Non-parallel sides may or may not be equal in length.
        
        Consecutive angles are supplementary (their sum is 180 degrees).
      - Kite
        
        Two pairs of adjacent sides are equal in length.
        
        One pair of opposite angles is equal.
        
        Diagonals intersect at a right angle.
        
        One diagonal bisects the other.
  - - - If the sides are the same length and interior angles are equal, the figure is called a regular polygon
- - - - For example, if the area factor is 3, it means the second figure's area is three times larger than the first figure's area. Similarly, if the area factor is 0.5, it means the second figure's area is half the size of the first figure's area.
  - - - Congruent triangles are two triangles that have exactly the same shape and size. When two triangles are congruent, all their corresponding sides and angles are equal. In other words, the corresponding parts of congruent triangles are identical.
      - Side-Side-Side (SSS) Congruence
        
        If all three sides of one triangle are equal in length to the corresponding three sides of another triangle, then the two triangles are congruent.
      - Side-Angle-Side (SAS) Congruence
        
        If two sides and the included angle of one triangle are equal in length to two sides and the included angle of another triangle, then the two triangles are congruent.
      - Angle-Side-Angle (ASA) Congruence
        
        If two angles and the included side of one triangle are equal in measure to two angles and the included side of another triangle, then the two triangles are congruent.
      - Angle-Angle-Side (AAS) Congruence
        
        If two angles and a non-included side of one triangle are equal in measure to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
      - RHS
        
        If the hypotenuse and one leg of a right triangle are equal in length to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
- - - - When you have two equal chords in a circle, their midpoints coincide with the center of the circle. Since the perpendicular bisector of a chord passes through its midpoint and the midpoint coincides with the center of the circle, the perpendicular bisectors of the equal chords will also pass through the center of the circle.
- - - - The measure of an angle indicates how wide or narrow it is. Angles are typically measured in degrees (°)
    - - Acute Angle: An angle that measures less than 90 degrees (90°).
      - Right Angle: An angle that measures exactly 90 degrees (90°).
      - Obtuse Angle: An angle that measures more than 90 degrees (90°) but less than 180 degrees (180°).
      - Straight Angle: An angle that measures exactly 180 degrees (180°).
      - Reflex Angle: An angle that measures more than 180 degrees (180°) but less than 360 degrees (360°).
      - Vertical Angles
        
        When two lines intersect, the opposite angles formed at the intersection are called vertical angles. Vertical angles are congruent, meaning they have the same measure.
      - Adjacent Angles
        
        Adjacent angles are two angles that share a common vertex and a common side but have no interior points in common.
      - Corresponding Angles
        
        When two lines are crossed by another line (known as a transversal), the angles on the same side of the transversal and in corresponding positions relative to the two lines are called corresponding angles. Corresponding angles are congruent if the two lines are parallel.
      - Alternate Interior Angles and Alternate Exterior Angles
        
        These are pairs of angles formed by a transversal intersecting two parallel lines. Alternate interior angles are congruent, as are alternate exterior angles.
      - Interior Angles of a polygon
        
        The sum of the interior angles of an n-sided polygon (where n is the number of sides) can be calculated using the formula: Sum of Interior Angles = (n - 2) * 180°.
        
        Exterior angles of a polygon
        
        For a polygon with n sides, each exterior angle can be calculated using the formula:
        Each Exterior Angle = 360 degrees / n