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**2-5 Proving Angles Congruent**

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Vertical Angles Angles formed by opposite rays.

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**Adjacent Angles Angles that share a common side and a common vertex,**

but have no common interior points.

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

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

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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.

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**Looking at a Diagram When looking at a diagram, we can conclude:**

Vertical angles Adjacent angles Adjacent supplementary angles

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**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)

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**What can you conclude from the diagram?**

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**Angle Investigation Draw two intersecting lines.**

Number the angles as shown. Use a protractor to measure each angle. Make a conjecture about vertical angles.

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Find the value of x

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Find the value of x

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**Congruent Complements Theorem**

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

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**Congruent Supplements Theorem**

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

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**All right angles are congruent.**

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**Congruent and Supplementary**

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**Find the value of both variables.**

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Find the value of x.

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**Find the measure of each angle.**

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**Find the measure of each angle.**

m1 m2 m3 m4

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Proving Angles Congruent. Vertical Angles: Two angles whose sides form two pairs of opposite rays; form two pairs of congruent angles 1 2 3 4 <1 and.

Proving Angles Congruent. Vertical Angles: Two angles whose sides form two pairs of opposite rays; form two pairs of congruent angles 1 2 3 4 <1 and.

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