Geometry Semester 1 Final Exam 1-15

Front

What is the slope of a line that is perpendicular to a line with slope m = \frac{3}{4}?

Back

The slope of a line that is perpendicular to a line with slope \frac{3}{4} is \frac{-4}{3}.

Front

How do you find the midpoint between two points G(-1, 2) and H(-3, -4)?

Back

The midpoint M is calculated using the formula M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right). For G and H, M = \left(\frac{-1 + (-3)}{2}, \frac{2 + (-4)}{2}\right) = (-2, -1).

Front

What postulate can be used to prove that two triangles are congruent if two sides and the included angle are known?

Back

The postulate is SAS (Side-Angle-Side).

Front

If one side of a triangle is missing, and the other two sides are 5 cm and 12 cm, what is the length of the missing side if it is a right triangle?

Back

Using the Pythagorean theorem, the missing side is 13 cm.

Front

In a parallelogram, if one angle is 2x + 10 and the adjacent angle is 3x - 20, how do you solve for x?

Back

Set the angles equal to 180 degrees: 2x + 10 + 3x - 20 = 180. Solving gives x = 1.

Front

What is the formula for the area of a triangle?

Back

The area A of a triangle is given by A = \frac{1}{2} \times base \times height.

Front

What is the definition of a parallelogram?

Back

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length.

Front

How do you calculate the distance between two points (x1, y1) and (x2, y2)?

Back

The distance d is calculated using the formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.

Front

What is the definition of congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What is the relationship between the angles in a triangle?

Back

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