Question

name: tavon reeves date: class: 6 topic: main ideas/questions: measuring segments the distance between two points a and b be written as ____ or __. congruent segments if __, then the segments are congruent. this is written as ____.

Explanation:

MEASURING SEGMENTS

Step1: Recall segment length definition

The distance between two points \( A \) and \( B \) is the length of segment \( AB \), written as \( AB \) (or \( m\overline{AB} \), where \( m\overline{AB} \) denotes the measure of segment \( \overline{AB} \)). For the number line example with \( A \) at \( 7 \) and \( B \) at \( 3 \) (assuming the number line has integer markings), the length \( AB = |7 - 3| = 4 \) (using the absolute value of the difference of coordinates).

Step2: Apply to congruent segments

If two segments have the same length (e.g., \( AB = CD \)), then the segments are congruent. This is written as \( \overline{AB} \cong \overline{CD} \) (the symbol \( \cong \) means congruent).

Filling the Notes/Examples:

• "The distance between two points \( A \) and \( B \) be written as \( AB \) (or \( m\overline{AB} \)) or the length of \( \overline{AB} \)."
• For the first number line (A and B): \( AB = |7 - 3| = 4 \) (assuming A is at 7, B at 3).
• "If \( AB = CD \), then the segments are congruent. This is written as \( \overline{AB} \cong \overline{CD} \)." (For the second number line, if C is at 5 and D at 1, \( CD = |5 - 1| = 4 \), so \( AB = CD = 4 \), hence \( \overline{AB} \cong \overline{CD} \))

Answer:

• MEASURING SEGMENTS: The distance between two points \( A \) and \( B \) is written as \( AB \) (or \( m\overline{AB} \)) or the length of \( \overline{AB} \). For the example, \( AB = 4 \) (if \( A \) is at 7, \( B \) at 3).
• CONGRUENT SEGMENTS: If \( AB = CD \) (their lengths are equal), then the segments are congruent. This is written as \( \overline{AB} \cong \overline{CD} \). (For the example, \( CD = 4 \) (if \( C \) at 5, \( D \) at 1), so \( \overline{AB} \cong \overline{CD} \))