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Math A Review

Geometry

Perpendicular lines form right angles.
Adjacent angles:  angles next to each other
Complementary angles:  pair of angles whose sum is 90.
Supplementary angles:  pair of angles whose sum is 180.
Linear Pair:  adjacent angles whose sum is 180.
Vertical angles are equal.
Polygons

• 3 sides---triangle
• 4 sides---quadrilateral
• 5 sides---pentagon
• 6 sides---hexagon
• 8 sides---octagon

The sum of the interior angles of any polygon with n side = 180(n-2)
The sum of the exterior angles of any polygon with n sides = 360 degrees
Regular Polygons:  all sides and angles are equal in measure.
Triangles:  Sum of angles is 180.

• Isosceles triangles:  two legs equal, base angles are equal
• Right triangles: one right angle
• Scalene triangle: no sides equal
• Equilateral triangle:  all sides and angles are equal
• An exterior angle of a triangle is equal to the sum of the two remote interior angles.
• Angles opposite congruent sides are congruent in a triangle
• The sum of two sides of a triangle is greater than the third.
• The side opposite the largest angle is the longest side.
• The side opposite the smallest angle is the shortest side.
• Proving Triangles Congruent -SAS, ASA, SSS, AAS, HYP. LEG THEOREM (for right triangles only)
• Proving Triangles Similar- a.a. = a.a.

Parallel lines cut by a transversal

• Alt Int. Angles are Congruent
• Corresponding Angles are equal
• Two angles on the same side of the transversal in the interior are supplementary.

Quadrilaterals Sum of the angles of a quadrilateral is 360.

• Parallelograms
•  
  • Both prs. of opp. sides are congruent.
  • Both prs. of opp. sides are parallel.
  • Both prs. of opp. angles are congruent.
  • Consecutive angles are supp.
  • Diagonals bisect each other.
• Rectangles
•  
  • All of the properties of a parallelogram.
  • All angles are right.
  • Diagonals are congruent
• Rhombus
•  
  • All of the properties of a parallelogram.
  • All sides are congruent.
  • Diagonals are perpendicular
  • Diagonals bisect the angles
• Square
•  
  • All properties of a parallelogram, rectangle and a rhombus
• Trapezoid
•  
  • Only one pr of opp. sides are parallel.
• Isosceles Trapezoid
•  
  • Only one pr of opp. sides are parallel.
  • One pair of opp. sides are congruent.
  • Diagonals Congruent
• Quadrilaterals with congruent diagonals:  rectangle, square, and isosceles trapezoid

Pythagorean Theorem:    use to prove a right triangle or use to find a missing side of a right triangle.
 
Pythagorean Triples
3, 4, 5         5, 12, 13        8, 15, 17