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2-8: Proving Angle RelationshipsGeometry: Logic 2-8: Proving Angle Relationships
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≅<1Symmetric 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 ≅ <6Prove: <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
Proving Angles Congruent. Vertical Angles: Two angles whose sides form two pairs of opposite rays; form two pairs of congruent angles
Lesson 2 – 8 Proving Angle Relationships
Lesson 3-6 Congruent Angles. Ohio Content Standards:
Chapter 3 Parallel and Perpendicular Lines
2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.
Section 1.6 Pairs of Angles
Angle Pair Relationships
Section 2.7 PROVE ANGLE PAIR RELATIONSHIPS. In this section… We will continue to look at 2 column proofs The proofs will refer to relationships with angles.
Proving Angle Relationships
Proving Angle Relationships Section 2-8. Protractor Postulate Given and a number r between 0 and 180, there is exactly one ray with endpoint A, extending.
Angle Relationships Section 1-5 Adjacent angles Angles in the same plane that have a common vertex and a common side, but no common interior points.
Lesson 2.6 p. 109 Proving Statements about Angles Goal: to begin two-column proofs about congruent angles.
Chapter 2.7 Notes: Prove Angle Pair Relationships
SPECIAL PAIRS OF ANGLES. Congruent Angles: Two angles that have equal measures.
Chapter 2.7 Notes: Prove Angle Pair Relationships Goal: You will use properties of special pairs of angles.
2.4 Vertical Angles. Vertical Angles: Two angles are vertical if they are not adjacent and their sides are formed by two intersecting lines.
Geometry Section 1.6 Special Angle Pairs. Two angles are adjacent angles if Two angles are vertical angles if.
Vertical angles – are not adjacent, and their sides are formed by two intersecting lines 1 and 3 are vertical angles 2 and 4 are vertical angles.
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