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Chapters 1-8 Review - Coggle Diagram

- - - - A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
        
        A rhombus is a parallelogram with four congruent sides.
        
        A rectangle is a parallelogram with four right angles.
        
        A square is a parallelogram with four congruent sides and four right angles.
        
        A trapezoid is a quadrilateral with exactly one pair of parallel sides.
  - - - Parallelogram Angle Congruence: Opposite angles of a parallelogram are congruent.
        
        Parallelgoram Diagonal Bisecting Theorem: The diagonals of a parallelogram bisect each other.
        
        Parallel Lines and Transverse Segment Congruence: If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
    - - Proving a Quadrilateral is a Parallelogram using Side Congruence: If both pairs of oppostie sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
        
        Proving a Quadrilateral is a Parallelogram using Angle Congruence: If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
        
        Proving a Quadrilateral is a Parallelogram using Diagonal Bisectors: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
        
        Proving a Quadrilateral is a Parallelogram using Congruent/Parallel Side Pair: If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram.
  - - - (Theorem) The diagonals of a rhombus are perpendicular.
        
        (Theorem) The diagonals of a rectangle are congruent.
        
        (Theorem) If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.
        (Theorem) If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
        (Theorem) If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
  - - - (Theorem) The base angles of an isosceles trapezoid are congruent.
        (Theorem) The diagonals of an isosceles trapezoid are congruent.
        (Theorem) The diagonals of a kite are perpendicular.
  - - - Centering figures at the origin is also helpful when placing figures in the coordinate plane.
- - - - (Theorem) Pythagorean Theorem: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
        (Theorem) Converse of the Pythagorean Theorem: If the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.
        (Theorem) If the square of the lengths of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, the triangle is obtuse.
        (Theorem) If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, the triangle is acute.
  - - - (Theorem) 45 degree-45 degree-90 degree Theorem: In a 45 degree-45 degree-90 degreee triangle, both legs are congruent and the length of the hypotenuse is the square root of two times the length of a leg.
        (Thoerem) 30 degree-60 degreee-90 degree Triangle Theorem: In a 30 degree-60 degree-90 degree triangle, the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is the square root of 3 times the length of the shorter leg.
  - - - Cosine of angle A = leg adjacent to angle A divided by hypotenuse
      - sin x degrees=cos (90-x) degrees
  - - - The angle of depression isthe angle formed by the line of sight and the horizontal plane for an object below the horizontal.
  - - - A vector sum can show the result of vectors that occur in sequence.
        It can also show the result of vectors that act at the same time.
- - - - Important Vocab:
        The Midpoint an distance Formulas
        
        M=(x1+x2)/2 (same for Y)
        D= Square root of* (x2-x1) + (y2-y1)
  - - - Bisector: Line that divides something into 2 equal pieces.
  - - - Circum: around
        Altitude: Height of a triangle
  - - - Conditional: If A, than B
        Contrapositive: If not A, than not B
        
        Indirect Reasoning: Type of reasoning were all possibilities are thought of and considered and the useless ones are proved wrong. The remaining possibilities are then thought of as true.
  - - - Comparison Property of Inequality: If a = b + c and c > 0, then a > b
- - - - Properties of Proportions: a/b=c/d is equivalent to ad=bc, b/a=d/c, a/c=b/d, and (a+b)/b=(c+d)/d.
        
        Cross-Product Property: a/b=c/d is equivalent to ad=bc.
        
        In a scale drawing, the scale compares each length in the drawing to the actual length. The lengths used in a scale can be in different units.
  - - - Proportions can be used to find unknown lengths in similar polygons.
  - - - (Theorem) Side-Angle-Side Similarity Theorem: If an angle of one triangle is congruent to an angle of a second triangle, and the sides including the two angles are proportional, then the triangles are similar.
        (Theorem) Side-Side-Side Similarity Theorem: If the corresponding sides of two triangles are proportional, then the triangles are similar.
  - - - For any two positive numbers a and b, the geometric mean of a and b is the positive number x such that a/x=x/b. x is the square root of ab.
- - - - Pythagorean triple: A set of three whole numbers that are not zero (a, b. and c,). These contribute the the equation a^2 + b^2 = c^2
  - - - Tangent: