2-8: Proving Angle Relationships Geometry: Logic 2-8: Proving Angle Relationships

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Homework

Today Angle Addition Relationships Monday: Review

Recall Angle Addition Postulate

Recall Angle Addition Postulate: m<ABD+ m<DBC = m< ABC

Example 1 Given: m<1=56 and m<JKL=145 Prove: m<1=89 K 2 J 1 L

Theorems: Supplement Theorem: If two angles form a linear pair, then they are supplementary angles.

Theorems Complement Theorem: If the noncommon sides of two adjacent angles form a right angle, then the angles are complementary angles.

Example 2: Given: m<1=73 Prove: m<2=17 1 2

Properties Reflexive Property: <1≅<1 Symmetric Property: <1 ≅ <2 then <2 ≅ <1 Transitive Property: If <1 ≅ <2 and <2 ≅ <3 then <1 ≅ <3

Theorems: Congruent Supplements Theorem: Angles supplementary to the same angle or to congruent angles are congruent themselves.

Theorems Congruent Complements Theorem: Angles complementary to the same angle or to congruent angles are congruent themselves.

Theorems: Vertical Angles Theorem: If two angles are vertical angles, then they are congruent.

Example 3: Given: <1 and <2 are supplementary; <2 and <3 are supplementary Prove: <1 ≅ <3 1 2 3

Example 4: Given: 𝐷𝐵 bisects <ADC Prove: <2 ≅ <3 B A C 1 2 D

Theorems Perpendicular lines intersect to form ______________. All right angles are ________________ Perpendicular lines form ____________ adjacent angles.

Theorems Perpendicular lines intersect to form four right angles. All right angles are congruent Perpendicular lines form congruent adjacent angles.

Theorems Continued If two angles are congruent and supplementary, then each angle is ___________________ If two congruent angles form a linear pair, then they are ___________________

Theorems Continued If two angles are congruent and supplementary, then each angle is a right angle. If two congruent angles form a linear pair, then they are right angles.

Example 5: Given: <5 ≅ <6 Prove: <4 and <6 are supplementary 6 5 4

Proving Theorems: Prove that perpendicular lines intersect to form four right angles.

Practice Problems Try some on your own! As always call me over if you are confused!

Exit Ticket Given: <4 ≅ <7 Prove: <5 ≅ <6 5 6 4 7