2 8 Proving Angle Relationships New Reasons Angle

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2 -8: Proving Angle Relationships

2 -8: Proving Angle Relationships

New Reasons: • Angle Addition Postulate: If R is in the interior of <PQS,

New Reasons: • Angle Addition Postulate: If R is in the interior of <PQS, then m<PQR+m<RQS=m<PQS • Supplement Theorem: If two angles form a linear pair, then they are supplementary. • Definition of Supplementary: If <1 and <2 are supp. , then m<1+m<2=180 • Definition of Complemenatry: If <1 and <2 are comp. , then m<1+m<2=90 • Definition of a right angle: An < that measures 90 degrees. • Vertical angles are congurent.

Given: m<1=4 x, m<2=2 x-6, m<1 and m<2 are complementary. Prove: x=14 Statements 1)

Given: m<1=4 x, m<2=2 x-6, m<1 and m<2 are complementary. Prove: x=14 Statements 1) m<1=4 x, m<2=2 x-6, m<1 and m<2 are complementary. Reasons 1) 2) m<1+m<2=90 2) 3) 3) Substitution 4) 6 x-6=90 4) 5) 6 x=84 5) 6) 6) Division Property of Equality

Given: m<JGH=68 and <JGH and <HGI form a linear pair Prove: m<JGF=112 Statements Reasons

Given: m<JGH=68 and <JGH and <HGI form a linear pair Prove: m<JGF=112 Statements Reasons 1) m<JGH=68 and <JGH and <HGI form a linear pair 1) Given 2) 2) Supplement Theorem 3) m<JGH+m<HGI=180 3) 4) <HGI=<JGF 4) 5) 5) Def. of congruent 6) 68+m<HGI=180 6) 7) m<HGI=112 7) 8) 8)

Given: <ABC and <DBE are complementary. <ABD and <DBE are supplementary. Prove: <CBD is

Given: <ABC and <DBE are complementary. <ABD and <DBE are supplementary. Prove: <CBD is a right angle. Statements Reasons 1) <ABC and <DBE are complementary. <ABD 1) and <DBE are supplementary. 2) m<ABC+m<CBD=m<ABD 2) 3) 3) Def. of complementary 4) 4) Def. of supplementary 5) m<ABC+m<CBD+m<DBE=180 5) 6) 6) Substitution 7) m<CBD=90 7) 8) <CBD is a right angle. 8)

Try p. 111; #6 Assignment tonight: Quiz review sheet

Try p. 111; #6 Assignment tonight: Quiz review sheet