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2-5 Proving Angles Congruent

2-5 Proving Angles Congruent. Vertical Angles. Angles formed by opposite rays. Adjacent Angles. Angles that share a common side and a common vertex, but have no common interior points. Complementary Angles. Two angle whose measures have a sum of 90 degrees.

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2-5 Proving Angles Congruent

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  1. 2-5 Proving Angles Congruent

  2. Vertical Angles • Angles formed by opposite rays.

  3. Adjacent Angles • Angles that share a common side and a common vertex, but have no common interior points.

  4. Complementary Angles • Two angle whose measures have a sum of 90 degrees. • or

  5. Supplementary Angles • Two angles whose measures have a sum of 180 degrees. • or

  6. Identify the Angles Name a pair of vertical angles. Name a pair of adjacent Angles. Name a pair of complementary angles. Name a pair of supplementary angles.

  7. Looking at a Diagram When looking at a diagram, we can conclude: • Vertical angles • Adjacent angles • Adjacent supplementary angles

  8. We cannot assume: • Angles or segments are congruent • Angles are right angles • Lines are parallel or perpendicular (unless there are marks that give this information)

  9. What can you conclude from the diagram?

  10. Angle Investigation • Draw two intersecting lines. • Number the angles as shown. • Use a protractor to measure each angle. • Make a conjecture about vertical angles.

  11. Find the value of x

  12. Find the value of x

  13. Congruent Complements Theorem If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent.

  14. Congruent Supplements Theorem If two angles are supplementary to the same angle (or congruent angles), then the two angles are congruent.

  15. All right angles are congruent.

  16. Congruent and Supplementary

  17. Find the value of both variables.

  18. Find the value of x.

  19. Find the measure of each angle.

  20. Find the measure of each angle. m1 m2 m3 m4

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