Chapter 6 Check Your Knowledge

For questions 1-5, state the property of equality or congruence that represents the given statement. If 4x = 16, then x = 4.

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

For questions 1-5, state the property of equality or congruence that represents the given statement: 2x + 1 = 2x + 1.

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

For questions 1-5, state the property of equality or congruence that represents the given statement. If y = 3x + 4 and y = 5, then 5 = 3x + 4.

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

• Reflexive Property

• Symmetric Property

• Transitive Property

• Substitution Property

Complete the two-column proof below. Given: m∠BAD = 97°, m∠CAD = 32°. Prove: m∠BAC = 65°. Fill in the blank for Statement 1.

e

f

g

h

Given

m∠BAC = m∠CAD - m∠BAD

Substitution Property of Equality

Transitive Property of Equality

m∠BAC = m∠BAD + m∠CAD

m∠BAC = m∠BAD / m∠CAD

m∠BAC = m∠BAD - m∠CAD

Fill in the missing steps in the flowchart proof to prove that m∠GFH = m∠IFJ. Given: m∠GFI = m∠HFJ. Prove: m∠GFH = m∠IFJ. Use the diagram to assist in filling the blanks.

e

f

g

h

m∠HFJ = m∠IFJ

m∠GFI = m∠IFJ

m∠GFH = m∠IFJ

Addition Property

m∠GFI = m∠GFH

Subtraction Property

Transitive Property

We are given that l bisects SU. By the Segment Addition Postulate,​ (a)   . By the definition of ​ (b)   , ST ≅ TU. Congruent segments have equal length, so ​ (c)   . Substituting this into ST + TU = SU gives ST = 1 2 SU.

• ST+TU=SU
• Segment Bisector
• ST=TU
• ST+SU=TU
• Segment Divider
• ST=2SU

Identify the missing statements in the proof.

a

b

c

Division Property

Subtraction property

Transitive property of congruence