Geometry Fall 24 Final Exam Review

The distance formula is derived from the Pythagorean Theorem and is used to calculate the distance between two points in a coordinate plane. It is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ .

AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It is expressed as: $$c^2 = a^2 + b^2$$ .

In a kite, the angles between the unequal sides are equal, and the diagonals intersect at right angles.

The sum of the interior angles of a triangle is always 180 degrees.

In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (they add up to 180 degrees).

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

To find the measure of an unknown angle in a triangle, subtract the sum of the known angles from 180 degrees. For example, if angles A and B are known, then angle C can be found using: $$C = 180 - (A + B)$$ .

The area (A) of a triangle can be calculated using the formula: $$A = \frac{1}{2} \times base \times height$$ .

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.