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Warm-up 2.5

Warm-up 2.5. Fill in the blank Perpendicular lines are two lines that intersect to form _______. An angle is formed by two rays with the same endpoint. The endpoint is called the _________ of the angle. 2.5 Proving Angles Congruent. Gonzales Geometry. Definitions. Vertical Angles

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Warm-up 2.5

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  1. Warm-up 2.5 Fill in the blank Perpendicular lines are two lines that intersect to form _______. An angle is formed by two rays with the same endpoint. The endpoint is called the _________ of the angle.

  2. 2.5 Proving Angles Congruent Gonzales Geometry

  3. Definitions • Vertical Angles • Two angles whose sides form two pairs of opposite rays

  4. definitions • Adjacent angles • Two coplanar angles with a common side, a common vertex, and no common interior points

  5. Definitions • Complementary Angles • Two angles whose measures have a sum of 90 degrees. • Each angle is called the complement of the other

  6. Definitions • Supplementary Angles • Two angles whose measures have a sum of 180 degrees • Each angle is called the supplement of the other.

  7. definitions • Theorem • Statements that have been mathematically proven true. • Paragraph proof • Written as sentences in a paragraph

  8. Theorems • Vertical Angle Theorem • Vertical angles are congruent • Congruent Supplements theorem • If two angles are supplements of the same angle (or of congruent angles), then the two angles are congruent. • Congruent Complements theorem • If two angles are complements of the same angle (or of congruent angles), then the two angles are congruent.

  9. Theorems • Theorem 2-4 • All right angles are congruent • Theorem 2-5 • If two angles are congruent and supplementary, then each is a right angle.

  10. Proving Angles Congruent LESSON 2-5 Additional Examples Find the value of x. The angles with labeled measures are vertical angles because their sides are opposite rays. Apply the Vertical Angles Theorem to find x. 4x – 101 = 2x + 3 Vertical Angles Theorem 4x = 2x + 104 Addition Property of Equality 2x = 104 Subtraction Property of Equality x = 52 Division Property of Equality Quick Check

  11. Proving Angles Congruent LESSON 2-5 Additional Examples Write a paragraph proof using the given, what you are to prove, and the diagram. Given: WX = YZ Prove: WY = XZ Proof: It is given that WX = YZ. Adding the middle segment, XY, to each smaller segment gives WX + XY = YZ + XY. By the Segment Addition Postulate, WX + XY = WY, and XY + YZ = XZ. Using substitution, you get WY = XZ. Quick Check

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  14. Assignment • Pg. 100 • 1-22 47-52

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