1. Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays. In this example the legs are AD and AE. A D E

2. Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays. In this example the legs are AD and AE. The measure of the angle “r” is in degrees. A D E r

3. Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays. In this example the legs are AD and AE. The measure of the angle “r” is in degrees. “A” is the vertex of the angle. A D E r

4. Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays. In this example the legs are AD and AE. The measure of the angle “r” is in degrees. “A” is the vertex of the angle. In geometry, figures are congruent if : - they have the same angle - they lie on the same lines - they pass through the same points A D E r

5. Introduction to Geometry – Congruent Angles Every angle has two sides ( or legs ) created by rays. In this example the legs are AD and AE. The measure of the angle “r” is in degrees. “A” is the vertex of the angle. In geometry, figures are congruent if : - they have the same angle - they lie on the same lines - they pass through the same points So two angles could be congruent even though their rays have different lengths. A D E r A B

6. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡.

7. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent.

8. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent. Definition – angles that lie on the same lines are congruent

9. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent. Definition – angles that lie on the same lines are congruent You can see the angles lie on the same lines…

10. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent. Definition – angles with legs that pass through the same points are congruent B AD C E

11. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent. Definition – angles with legs that pass through the same points are congruent You can see the angles pass through the same points… B AD C E When naming angles using points, the vertex is in the middle

12. Introduction to Geometry – Congruent Angles The symbol for congruence is ≡. Sides can be congruent. Angles can be congruent. Figures can be congruent. Definition – angles with legs that pass through the same points have the same measurement. B AD C E

13. Introduction to Geometry – Congruent Angles Angle congruence theorems : ANGLE IDENTITY Theorem : - Any angle is congruent to itself A C B

14. Introduction to Geometry – Congruent Angles Angle congruence theorems : ANGLE IDENTITY Theorem : - Any angle is congruent to itself RIGHT ANGLE CONGRUENCE Theorem : - Any two right angles are congruent - a right angle = 90° A C B B C A E D F

15. Introduction to Geometry – Congruent Angles Angle congruence theorems : ANGLE IDENTITY Theorem : - Any angle is congruent to itself RIGHT ANGLE CONGRUENCE Theorem : - Any two right angles are congruent - a right angle = 90° STRAIGHT ANGLE CONGRUENCE Theorem : - any two straight angles are congruent - a straight angle is a straight line and = 180° A C B B C A E D F Q PR YZX