Alternate Interior Angles are a pair of angles formed by two lines and a transversal and are located on opposite sides of the transversals and inside or between (on the interior of) the two lines.

3 & 5 and 4 & 6 are alternate interior angles.

Theorem: If the lines are parallel, alternate interior angles are congruent.

3 @ 5 and 4 @ 6

Alternate exterior angles are a pair of angles formed by two lines and a transversal and are located on opposite sides of the transversals and outside (on the exterior of) the two lines.

1 & 7 and 2 & 8 are alternate interior angles.

Theorem: If the lines are parallel, alternate exterior angles are congruent.

1 @ 7 and 2 @ 8

Area The number of square units that cover a shape or surface.

Arrow diagram A diagram using arrows to show logical connections. An arrow diagram can be used in place of an if, then statement:

If P, then Q is equivalent to P Q

Base A side of a polygon. The base is the side perpendicular to the height of the polygon. In a trapezoid, the bases are the two parallel sides.

Complementary angles Any two angles whose measures add to 90 degrees.

Conditional statement A statement in the form, If P, then Q where P is the hypothesis and Q is the conclusion.

Conjecture A statement that has not been proved.

Corresponding angles are a pair of angles formed by two lines and a transversal and are located in the same quadrant formed by the intersection of the transversal and one of the lines.

1 & 5, 2 & 6, 3 & 7, and 4 & 8 are corresponding angles.

Postulate: If the lines are parallel, corresponding angles are congruent.

1 @ 5 2 @ 6 3 @ 7 4 @ 8

Dimensions The measurements of the lengths of the sides, base, altitude, height, radius, circumference, perimeter, apothem, angles, slant heights, and any other parts of a shape.

Height The altitude, or perpendicular segment from a vertex to the line containing the opposite side, or base, of a polygon.

Hypotenuse The longest side of a right triangle.

The side of a triangle that is opposite the right angle.

Leg The sides forming the right angle in a right triangle. The non-parallel sides of a trapezoid. The two congruent sides of an isosceles triangle.

Line A line is straight, infinitely long, and has no width.

Parallelogram A quadrilateral with two pair of parallel sides.

A quadrilateral whose diagonals bisect each other.

A quadrilateral with two pairs of congruent opposite sides.

Perimeter The distance around a shape.

Proof by contradiction To assume the reverse of what is to be proved, show it is impossible by contradicting a known fact, thus proving that the opposite must be true.

Pythagorean Theorem In a right triangle, the sum of the squares of the legs equals the square of the hypotenuse.

Rectangle

A quadrilateral with 4 right angles.

A quadrilateral with congruent diagonals that bisect each other.

A quadrilateral with 2 pairs of parallel sides and a right angle.

A parallelogram with a right angle.

A parallelogram with congruent diagonals.

Right angle An angle with measure 90 degrees.

Same-side interior angles are a pair of angles formed by two lines and a transversal and are located on the same side of the transversals and between (on the interior of) the two lines.

3 & 6 and 4 & 5 are same-side interior angles.

t

 

Theorem: If the lines are parallel, same side interior angles

are supplementary.

4 and 5 are supplementary.

3 and 6 are supplementary.

Square The geometric shape:

A quadrilateral with 4 congruent sides and 4 right angles.

A rectangle with 2 adjacent congruent sides.

A parallelogram with a right angle and 2 adjacent congruent sides.

A rhombus with a right angle.

A parallelogram with diagonals that are perpendicular and congruent.

The numerical value:

A number that is the product of two identical real numbers.

(3)(3) = 9, so 9 is the square of 3.

The square of the side of a square gives the Area of the square.


 

Square root The number, when multiplied by itself, that equals a given number is called the square root of that number.

(3)(3) = 9, so 3 is the square root of 9.

The square root of the area of a square gives the length of the side of the square.

Straight angle A straight angle is an angle whose sides form a line and whose measure is 180.

AVC is a straight angle.

mAVC = 180

Definition: A straight angle pair is two angles adjacent angles whose exterior sides form a straight line. 1 and 2 are a straight angle pair.

Theorem: The sum of the measures of a straight angle pair equals 180.

m1 + m2 = 180

Theorem: A straight angle pair is supplementary.

Supplementary angles

Supplementary angles are any two angles whose measures add to 180.

Theorem A statement that has been proved using logic, deductive reasoning, postulates, definitions, and previously proved theorems, and rules of algebra.

Transversal A line that intersects two other lines in two distinct points. Line t is the transversal of lines m and n.

Trapezoid A quadrilateral with exactly one pair of parallel sides.

Triangle Inequality Theorem In a triangle, the third side of the triangle is greater than the difference of the other two sides and at the same time is less than the sum of the other two sides.

|a b| < c < a + b

for a, b, c sides of a triangle.

Unit of measure A defined length, such as 1 inch or 1 kilometer, that is used to measure the distance between two points.

Vertical angles Vertical angles are formed by two intersecting lines. Vertical angles share a common vertex but no common sides.

1 and 3 are vertical angles.

2 and 4 are vertical angles

Theorem: Vertical angles are congruent.

1 @ 3

2 @ 4