Proving Angles Congruent

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Presentation transcript:

Proving Angles Congruent

1 4 3 2 Types of Angles Vertical Angles Two angles whose sides form two pairs of opposite rays. 1 4 3 2

Types of Angles Adjacent Angles Two coplanar angles with a common side, a common vertex, and NO common interior points. 1 2

Types of Angles Complementary Angles Two angles who measures have a sum of 90˚ 1 2

Types of Angles Supplementary Angles Two angles who measures have a sum of 180˚. 1 2

Identifying angle pairs Which pair of angles are complementary? Which pair of angles are supplementary? Which pair of angles are vertical? Which pair of angles are adjacent? 1 2 3 4 5

Conclusions you can make looking at or drawing a diagram… You CAN assume that angles are… Adjacent angles Adjacent supplementary angles Vertical angles You CANNOT assume that… Angles or segments are congruent Angles are right angles Lines are parallel or perpendicular

What CAN you conclude from the diagram? 3 2 4 5 1 by the Angle Addition Postulate. are vertical angles. are adjacent angles. are adjacent supplementary angles.

Theorem 2 – 1 Vertical Angles Theorem Vertical angles are congruent 1 2 3 4

Theorem 2-2 If two angles are supplements of the same angle(or of congruent angles), then the two angles are congruent Theorem 2-3 If two angles are complements of the same angle ( or of congruent angles), then the two angles are congruent.

Theorem 2 -4 All right angles are congruent. Theorem 2 – 5 If two angles are congruent AND supplementary, then each angle is a right angle. 1 2