Geometry Fall Semester Exam

Front

What are complementary angles?

Back

Complementary angles are two angles whose measures add up to 90 degrees.

Front

If \( m\angle P = 7x + 3 \) and \( m\angle Q = 16x + 5 \), how do you find \( m\angle P \) if they are complementary?

Back

Set up the equation: \( (7x + 3) + (16x + 5) = 90 \). Solve for \( x \) and substitute back to find \( m\angle P \).

Front

What is the slope of a line perpendicular to another line with slope \( m \)?

Back

The slope of a line perpendicular to another line with slope \( m \) is \( -\frac{1}{m} \).

Front

If \( \overline{KM} \) is the perpendicular bisector of \( \overline{JL} \), what does this imply about the segments?

Back

It implies that \( KM = ML \) and that \( KM \) is perpendicular to \( JL \).

Front

How do you find the midpoint of a line segment?

Back

The midpoint \( M \) of a line segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Front

If \( K \) is the midpoint of \( \overline{JL} \), and \( JK = 9x - 1 \) and \( KL = 2x + 27 \), how do you find \( JL \)?

Back

Set \( JK = KL \) because they are equal. Solve for \( x \) and then use \( JL = JK + KL \).

Front

What is the definition of a perpendicular bisector?

Back

A perpendicular bisector of a segment is a line that divides the segment into two equal parts at a 90-degree angle.

Front

How do you solve for an unknown in an equation involving angles?

Back

Isolate the variable by using algebraic operations, then substitute back to find the angle measures.

Front

What is the relationship between the slopes of two perpendicular lines?

Back

The product of the slopes of two perpendicular lines is -1.

Front

If two angles are complementary, what is the sum of their measures?

Back

The sum of the measures of two complementary angles is 90 degrees.