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Transcript
Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then mABC mABD mDBC A D B C Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then mABC mABD mDBC A D A 50° B In this example : mABC 50 75 mABC 125 75° C Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then mABC mABD mDBC A D 50° 75° B In this example : C mABC 50 75 mABC 125 A straight angle is formed by two rays going away from each other. It measures 180°. 180° B A C Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then mABC mABD mDBC A D A 50° 75° B In this example : C mABC 50 75 mABC 125 A straight angle is formed by two rays going away from each other. It measures 180°. Draw a third ray and you have a linear pair. This linear pair forms a straight line, they are supplementary angles and add up to 180°. D B A C Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° These pairs should all add up to 180° Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° 120 ° These pairs should all add up to 180° Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° 120° 155° These pairs should all add up to 180° Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° 120° 155° 25° These pairs should all add up to 180° Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° 120° 155° 25° 42° 174° 76° * * * These pairs should all add up to 180° See if you can get the last three on your own before moving to the next page… Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180° EXAMPLE : Let’s fill in the table with the missing supplementary angle. Angle 1 Angle 2 60° 120° 155° 25° 42° 138° 174° 6° 76° 104° These pairs should all add up to 180° See if you can get the last three on your own before moving to the next page… Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° 50° 40° Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° These pairs should all add up to 90° Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° 30° These pairs should all add up to 90° Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° 30° 45° These pairs should all add up to 90° Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° 30° 45° 45° These pairs should all add up to 90° Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° 30° 45° 45° 27° 79° 16° * * * These pairs should all add up to 90° See if you can get the last three on your own before moving to the next page… Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° EXAMPLE : Let’s fill in the table with the missing complementary angle. Angle 1 Angle 2 60° 30° 45° 45° 27° 63° 79° 11° 16° 74° These pairs should all add up to 90° See if you can get the last three on your own before moving to the next page… Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines B C E A D Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side B C E A D BEC and AED Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side B C E A D BEC and AED BEA and CED Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side B C E A D BEC and AED BEA and CED Vertical angles are also congruent BEC AED BEA CED Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ? Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ∟CQD Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ∟CQD ∟FQC Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE ∟FQD Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C Q A D E Find the partner for the given angle to make a vertical angle pair. Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE ∟FQD ∟BQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 50° Q A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = ? ∟FQC ∟AQE ∟FQD ∟BQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 50° Q 50° A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC ∟AQE ∟FQD ∟BQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 38° Q A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = ? ∟FQD ∟BQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 38° 38° Q A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD ∟BQE Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 136° Q A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD = 136° ∟BQF = ? Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines F B C 44° 136° Linear pair Q A D E Complete the table with the missing measurement. Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD = 136° ∟BQF = 44°
