Introduction to geometry
- 1. Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then A D B C DBCABDABC mmm +=
- 2. Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then A D B C DBCABDABC mmm += A 50° 75° In this example : °= °+°= 125ABC 7550ABC m m
- 3. Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then A D B C DBCABDABC mmm += A 50° 75° In this example : °= °+°= 125ABC 7550ABC m m A straight angle is formed by two rays going away from each other. It measures 180°. 180° B C
- 4. Introduction to Geometry – Complimentary / Supplementary Angles Angle Addition Postulate – If D is a point interior to angle ABC, then A D B C DBCABDABC mmm += A 50° 75° In this example : °= °+°= 125ABC 7550ABC m m 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°. B A C D
- 5. Introduction to Geometry – Complimentary / Supplementary Angles Supplementary Angles – formed by a linear pair and add up to 180°
- 6. 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°
- 7. 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°
- 8. 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°
- 9. 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°
- 10. 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…
- 11. 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…
- 12. Introduction to Geometry – Complimentary / Supplementary Angles Complementary Angles – two angles that form a right angle and add up to 90° 40° 50°
- 13. 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°
- 14. 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°
- 15. 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°
- 16. 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°
- 17. 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…
- 18. 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…
- 19. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB
- 20. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side A E D CB AEDBEC ∠∠ and
- 21. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side A E D CB AEDBEC ∠∠ and CEDBEA ∠∠ and
- 22. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines and on the opposite side A E D CB AEDBEC ∠∠ and CEDBEA ∠∠ and Vertical angles are also congruent CEDBEA AEDBEC ∠≡∠ ∠≡∠
- 23. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angleFind the partner for the given angle to make a vertical angle pair. Q
- 24. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ? Find the partner for the given angle to make a vertical angle pair. Q
- 25. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ∟CQD Find the partner for the given angle to make a vertical angle pair. Q
- 26. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ∟CQD ∟FQC Find the partner for the given angle to make a vertical angle pair. Q
- 27. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE Find the partner for the given angle to make a vertical angle pair. Q
- 28. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE ∟FQD Find the partner for the given angle to make a vertical angle pair. Q
- 29. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA ∟CQD ∟FQC ∟AQE ∟FQD ∟BQE Find the partner for the given angle to make a vertical angle pair. Q
- 30. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = ? ∟FQC ∟AQE ∟FQD ∟BQE Complete the table with the missing measurement. Q 50°
- 31. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC ∟AQE ∟FQD ∟BQE Q 50°50° Complete the table with the missing measurement.
- 32. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = ? ∟FQD ∟BQE Q 38° Complete the table with the missing measurement.
- 33. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD ∟BQE Q 38° 38° Complete the table with the missing measurement.
- 34. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD = 136° ∟BQF = ? Q 136° Complete the table with the missing measurement.
- 35. Introduction to Geometry – Complimentary / Supplementary Angles Vertical Angles – angles formed by two intersecting lines A E D CB F Given angle Vertical angle ∟BQA = 50° ∟CQD = 50° ∟FQC = 38° ∟AQE = 38° ∟FQD = 136° ∟BQF = 44° Q 136° Complete the table with the missing measurement. 44° Linear pair