Proving Statements About Angles

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Presentation transcript:

Proving Statements About Angles Chapter 2 Section 2.6-Part 1 Proving Statements About Angles

Warm-Up Find the measure of each angle. A right angle 90° The complement of 42° 48° The supplement of 42° 138° Two congruent angles that are complementary 45° and 45° Two congruent angles that are supplementary 90° and 90°

Definitions

A mA = 90° A mA < 90° A is acute A 90° < mA < 180° A is obtuse

Use the diagram to decide whether the statement is true or false True Vertical Angles  False: 60, 60, 120, 120 True: Both pairs are linear pairs and = 180

Make sketch of the given information label all angles that can be determined 42° 48° 42° 138°

Make sketch of the given information label all angles that can be determined 90° 42° 138° 42° 138°

Solve for x Vertical Angles are  Linear Pairs are Supplementary 4x – 17 = 2x + 9 2x – 17 = 9 2x = 26 x = 13 Linear Pairs are Supplementary 7x + 2 + 3x + 8 = 180 10x + 10 = 180 10x = 170 x = 10

Solve for x Vertical Angles are  3x – 5 = 79 3x = 84 x = 28

1. Given 2. Def. of Complementary Angles 3. Given 4. Def.  Angles 5. Substitution 6. Substitution 7. Def. of Complementary Angles

Write a Two Column Proof Statements Reasons 1. 2  3 1. Given 2. 1  2 4  3 2. Vertical Angles are  3. 1  3 3. Transitive 4. 1  4 4. Transitive