Exploring Segment Addition and Subtraction Axioms

What is the primary conclusion you can draw from knowing a point is the midpoint of a segment?

• The segment is divided into two equal parts.

• The segment is divided into three equal parts.

• The segment is divided into unequal parts.

• The segment is divided into four equal parts.

According to the Segment Addition Postulate, if AB = 4 cm and BC = 10 cm, what is the length of AC?

• 4 cm

• 14 cm

• 6 cm

• 10 cm

If AB is congruent to CD and EF is added to both, what can be said about the sums AB + EF and CD + EF?

• They are half the length of EF.

• They are equal.

• They are not equal.

• They are double the length of EF.

Using the Segment Subtraction Postulate, if AC = 14 cm and BC = 10 cm, what is the length of AB?

• 14 cm

• 24 cm

• 10 cm

• 4 cm

What does the Subtraction Axiom of Equality state?

• If a segment is added to two congruent segments, the sums are congruent.

• If a segment is subtracted from two congruent segments, the differences are not congruent.

• If a segment is subtracted from two congruent segments, the differences are congruent.

• If a segment is added to two congruent segments, the sums are not congruent.

What does the Reflexive Property state about a segment?

• A segment is congruent to another segment.

• A segment is equal to the sum of its parts.

• A segment is congruent to itself.

• A segment is not congruent to itself.

In a proof, if you need to state that a segment NP is congruent to itself, which property would you use?

• Substitution Property

• Reflexive Property

• Segment Subtraction Postulate

• Segment Addition Postulate

What is the purpose of the Substitution Property in proofs?

• To add segments together.

• To swap out segments or values that are congruent.

• To subtract segments from each other.

• To state that a segment is congruent to itself.

If AB is congruent to EF and AB + CD = GH, what can you substitute for AB in the equation?

• EF

• GH

• CD

• None of the above

When deciding whether to use addition or subtraction in a proof, what should you compare?

• The number of segments.

• The given segments to the segments you need to prove.

• The lengths of the segments.

• The type of segments.