Geometry Mid-Term Exam Fall '24

Front

What is the formula to find the distance between two points \(X(x_1, y_1)\) and \(Y(x_2, y_2)\)?

Back

The distance \(\overline{XY}\) is given by the formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Front

Define an isosceles triangle.

Back

An isosceles triangle is a triangle that has at least two sides of equal length.

Front

What is the sum of the interior angles of a triangle?

Back

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

Front

How do you classify triangles based on their angles?

Back

Triangles can be classified as acute (all angles < 90°), right (one angle = 90°), or obtuse (one angle > 90°).

Front

What are vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Front

If \(m\angle1 = (6x + 11)\degree\) and \(m\angle2 = (10x - 9)\degree\), how do you find \(m\angle1\)?

Back

Set \(m\angle1 = m\angle2\) because they are vertical angles, then solve for \(x\) and substitute back to find \(m\angle1\).

Front

What is the Pythagorean theorem?

Back

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

Front

How do you find the value of \(x\) in a linear equation?

Back

To find \(x\), isolate it on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.

Front

What is the formula for the area of a triangle?

Back

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

Front

What is a scalene triangle?

Back

A scalene triangle is a triangle in which all three sides are of different lengths.