Triangle Proofs With Addition/Subtraction/Substitution Postulate

What does the addition postulate state?

• Equal quantities can only be added to unequal quantities.

• Adding different quantities results in equal sums.

• If equal quantities are added to equal quantities, the sums are equal.

• If equal quantities are added to equal quantities, the sums are different.

What principle allows a quantity to be replaced with its equal in any expression?

• Congruence postulate

• Addition postulate

• Subtraction postulate

• Substitution postulate

What does the substitution postulate allow in geometric proofs?

• To only substitute numbers for geometric figures.

• To substitute a quantity with its equal in any expression.

• To substitute a quantity with its unequal in any expression.

• To replace a longer segment with a shorter one.

In proving triangle congruence, what property states that a segment is congruent to itself?

• Addition property

• Substitution property

• Symmetric property

• Reflexive property

How can the subtraction postulate be used in geometric proofs?

• To prove that subtracting unequal quantities from equal quantities results in equal differences.

• To argue that subtracting equal quantities from unequal quantities results in unequal differences.

• To demonstrate that adding equal quantities results in equal sums.

• To show that subtracting equal quantities from equal quantities results in equal differences.

What theorem is used to prove the congruence of larger segments from congruent smaller segments?

• Segment Addition Theorem

• Segment Subtraction Theorem

• Reflexive Property

• Side-Side-Side (SSS) Theorem

Which property is used to state that a segment or angle is congruent to itself?

• Angle Addition Theorem

• Reflexive Property

• Segment Addition Theorem

• Transitive Property

What criteria was initially identified as a potential way to prove the triangles congruent in the first example?

• Side-Angle-Side (SAS)

• Angle-Side-Angle (ASA)

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

In the second example, what theorem is suggested to prove the congruence of smaller angles from larger congruent angles?

• Reflexive Property

• Segment Subtraction Theorem

• Angle Addition Theorem

• Angle Subtraction Theorem

What proof strategy is proposed for the second set of triangles based on the given information?

• Angle-Angle-Side (AAS)

• Side-Side-Side (SSS)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)