Property of Equality Definition Addition Property Subtraction Property

Property of Equality Definition Addition Property Subtraction Property Multiplication Property Division Property Substitution Property Reflexive Property Symmetric Property Transitive Property If a = b, then b = a If a = b and c = d, then a + c = b + d. If a = b and b = c, then a = c a=a If a = b and c = d, then a – c = b – d. If a = b, then either a or b may be substituted for the other in any equation (or inequality) If a = b, then ca = cb Intro to Proofs- Engage

Property of Congruence Definition Reflexive Property Symmetric Property Transitive Property Intro to Proofs- Engage

Solve: Statements Reasons 1. Given equation 2. 3. Addition Property of Equality 4. Intro to Proofs- Explore

Given: RT and PQ intersecting at S so that RS = PS and ST = SQ Prove: RT = PQ R P S T Q Statements Reasons 1. RS = PS; ST = SQ 1. Given 2. RS + ST = PS + SQ 2. 3. RS + ST = RT; PS + SQ = PQ 3. 4. Substitution Property Intro to Proofs- Explore

Given: m ∠ AOC = m ∠ BOD Prove: m∠ 1=m∠ 3 B A 1 2 C 3 O Statements Reasons 1. Given 2. m ∠ AOC = m ∠ 1 + m ∠ 2; m ∠ BOD = m ∠ 2 + m ∠ 3 2. 3. m ∠ 1 + m ∠ 2 = m ∠ 2 + m ∠ 3 3. Substitution Property 4. 5. m ∠ 1 m∠ 2=m∠ 2 = m∠ 3 5. Intro to Proofs- Explore D

S Given: Prove: m ∠ 1 = m ∠ 2; m∠ 3=m∠ 4 P m ∠ SRT = m ∠ STR R 3 Q Z 1 Statements Reasons 1. Given 2. Addition Property of Equality 3. Angle Addition Postulate 4. Intro to Proofs- Explore 2 4 T