Question

identify the following statements as either true or false.

answer bank

• a perpendicular bisector is a ray, line, or line segment that divides a line segment into two equal segments and forms four right angles with the line segment.
• congruent segments have the same length.
• the symbol used to show congruence is: \\(\cong\\).
• a segment bisector bisects a line segment, creating two line segments with different lengths.
• a midpoint is the center point of a line segment.
• an angle bisector bisects an angle to create two angles with the same measurement.
• construction is the process of drawing a geometrical figure using a calculator.

Explanation:

Analyze definitions of bisectors and midpoints

Using the Geometric Definitions and Basic Geometry Vocabulary knowledge points:

• A perpendicular bisector divides a segment into two equal parts at a \(90^\circ\) angle, forming four right angles. This is true.
• Congruent segments have equal lengths by definition. This is true.
• A midpoint is the exact center point of a segment. This is true.
• An angle bisector divides an angle into two equal angles. This is true.

Analyze congruence symbol and segment bisector

Using the Basic Geometry Vocabulary knowledge point:

• The symbol for congruence is \(\cong\), not \(\cong\) with a line or other variations like \(\cong\) shown as \(\cong\). The image shows \(\cong\), which is correct.
• A segment bisector divides a segment into two equal lengths, not different lengths. Thus, the statement about different lengths is false.

Analyze construction definition

Using the Geometric Definitions knowledge point:

• Geometric construction is the process of drawing figures using only a straightedge and compass, without a calculator. Thus, the statement about using a calculator is false.

Answer:

true

• A perpendicular bisector is a ray, line, or line segment that divides a line segment into two equal segments and forms four right angles with the line segment.
• Congruent segments have the same length.
• The symbol used to show congruence is: \(\cong\).
• A midpoint is the center point of a line segment.
• An angle bisector bisects an angle to create two angles with the same measurement.

false

• A segment bisector bisects a line segment, creating two line segments with different lengths.
• Construction is the process of drawing a geometrical figure using a calculator.