Section2.4
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The document discusses three kinds of special angle pairs: complementary angles whose sum is 90 degrees, supplementary angles whose sum is 180 degrees, and vertical angles formed by two intersecting lines which are always congruent according to the Vertical Angle Theorem. It provides examples of each kind of special angle pair and introduces the Vertical Angle Theorem stating that vertical angles are congruent.
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G Nov3 P6
This document contains an agenda for a math class covering section 2.5 on proving angles congruent. The agenda includes reviewing notes on four theorems: [1] the vertical angle theorem which states that vertical angles are congruent, [2] the congruent supplements theorem which states that angles that are supplementary to the same angle are congruent, [3] the congruent complements theorem which states that angles that are complementary to the same angle are congruent, and [4] the right angle theorem which states that if two angles are congruent and supplementary, then each is a right angle. The class will review these notes, have an assessment on chapter 2, and begin chapter 3 material.
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This document contains notes from a geometry lesson on proving angles congruent. It includes an agenda for the class period which involves a vocabulary quiz, lesson on proving angles congruent using complementary angles, supplementary angles, vertical angles, adjacent angles, and linear pairs. It also includes proofs of several theorems including the vertical angle theorem, congruent supplements theorem, and congruent complements theorem. It concludes with an upcoming assessment schedule.
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This document contains notes from a geometry lesson on proving angles congruent. It includes 5 theorems:
1) The vertical angle theorem states that vertical angles are congruent.
2) The congruent supplements theorem states that if two angles are supplementary to the same angle, then they are congruent.
3) The congruent complements theorem states that if two angles are complementary to the same angle, then they are congruent.
4) The right angle theorem states that all right angles are congruent.
5) The congruent-supplementary theorem states that if two angles are congruent and supplementary, then each is a right angle.
The notes provide examples, definitions,
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The document introduces several key concepts about angles:
1) It defines an angle as the union of two rays with a common endpoint called the vertex.
2) It classifies angles as acute, right, or obtuse based on their measure.
3) It defines congruent angles, adjacent angles, and a linear pair of angles.
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This document contains an agenda for a math class covering section 2.5 on proving angles congruent. The agenda includes reviewing notes on four theorems: [1] the vertical angle theorem which states that vertical angles are congruent, [2] the congruent supplements theorem which states that angles that are supplementary to the same angle are congruent, [3] the congruent complements theorem which states that angles that are complementary to the same angle are congruent, and [4] the right angle theorem which states that if two angles are congruent and supplementary, then each is a right angle. The class will review these notes, have an assessment on chapter 2, and begin chapter 3 material.
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This document contains notes from a geometry lesson on proving angles congruent. It includes an agenda for the class period which involves a vocabulary quiz, lesson on proving angles congruent using complementary angles, supplementary angles, vertical angles, adjacent angles, and linear pairs. It also includes proofs of several theorems including the vertical angle theorem, congruent supplements theorem, and congruent complements theorem. It concludes with an upcoming assessment schedule.
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This document contains notes from a geometry lesson on proving angles congruent. It includes 5 theorems:
1) The vertical angle theorem states that vertical angles are congruent.
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3) The congruent complements theorem states that if two angles are complementary to the same angle, then they are congruent.
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1.5 notes
The document defines and provides examples of several angle pair relationships:
- Complementary angles have a sum of 90 degrees.
- Supplementary angles have a sum of 180 degrees.
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* There are 3 angles in a triangle
* The sum of the angles is 180°
* We are given: Angle 1 = 85°, Angle 2 = 60°
* So: Angle 1 + Angle 2 + Angle 3 = 180°
* 85° + 60° + Angle 3 = 180°
* 145° + Angle 3 = 180°
* Angle 3 = 180° - 145° = 35°
Therefore, the missing angle is 35°.
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Section2.4
- 1. Special Pairs of Angles Section 2-4
- 2. Three Kinds of “Special” Pairs 1. Complementary Angles (comp. ∠ ’s) – two angles whose sum is 90 degrees. D 60° 30° E F ∠ D and ∠ F are complementary ∠ F is a complement of ∠ D
- 3. Three Kinds of “Special” Pairs 2. Supplementary Angles (supp. ∠ ’s) – two angles whose sum is 180 degrees. 100° 80° X Z ∠ X and ∠ Z are supplementary ∠ X is a supplement of ∠ Z
- 4. So, what’s the difference between a linear pair and supplementary angles?
- 5. Three Kinds of “Special” Pairs 3. Vertical Angles (vert. ∠ ’s) – two nonadjacent angles formed by two intersecting lines 2 1 3 4 ∠ 1 and ∠ 3 are vertical angles ∠ 2 and ∠ 4 are vertical angles
- 6. And One New Theorem Vertical Angle Theorem (VAT) – Vertical angles are congruent. P• •L ∠ POL ≅ ∠ KOJ O J •K ∠ JOP ≅ ∠ LOK •
- 7. Complete with always, sometimes, or never 1. Vertical angles ____________ have a common vertex. 2. Two right angles are ____________ complementary. 3. Right angles are ____________ vertical angles. 4. Angles 1, 2, and 3 are ____________ complementary. 5. Vertical angles ____________ have a common supplement.