(Geometry) 1.1 Measuring Segments and Angles

Length of a segment

The distance between two points measured along a straight line.

Angle

A figure formed by two rays, called the sides of the angle, sharing a common endpoint called the vertex.

Protractor

An instrument used to measure angles in degrees.

Complementary angles

Two angles whose measures add up to 90 degrees.

Supplementary angles

Two angles whose measures add up to 180 degrees.

Congruent segments

Segments that have the same length.

Bisector

A line, ray, or segment that divides another segment or angle into two equal parts.

Find the length of a segment

Given points A(2, 3) and B(5, 7), calculate the distance between them using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. The length of segment AB is approximately 5 units.

Calculate the measure of angle

If angle A measures 40 degrees, what is the measure of its complementary angle? The measure of the complementary angle is 50 degrees.

Using a protractor

If angle B measures 120 degrees, what is the measure of its supplementary angle? The measure of the supplementary angle is 60 degrees.

Identify congruent segments

If segment AB is 4 cm and segment CD is also 4 cm, are segments AB and CD congruent? Yes, AB and CD are congruent because they have the same length.

Apply the Segment Addition Postulate

If segment AB is 3 cm and segment BC is 5 cm, what is the length of segment AC? According to the Segment Addition Postulate, AC = AB + BC = 3 cm + 5 cm = 8 cm.

Collinear points

Determine if points P(1, 2), Q(2, 4), and R(3, 6) are collinear. Yes, they are collinear because they lie on the same straight line.

Postulates in Geometry

Explain the importance of postulates in geometry. Postulates are fundamental truths used as a foundation for developing geometric theories, such as the Segment Addition Postulate which states that if point B lies on segment AC, then AB + BC = AC.