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GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #17 Practice Quiz Lesson: Homework / Questions Clean-up. Practice Quiz (~5 min). For each of these statements, name the postulate or theorem that justifies the statement: If x + 1 = 2 x , then 1 = x .

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gbk geometry

GBK Geometry

Jordan Johnson

today s plan
Today’s plan
  • Greeting
  • Review Asg #17
  • Practice Quiz
  • Lesson:
  • Homework / Questions
  • Clean-up
practice quiz 5 min
Practice Quiz (~5 min)
  • For each of these statements, name the postulate or theorem that justifies the statement:
    • If x + 1 = 2x, then 1 = x.
    • If x⁄3 – 6 = 3, then x⁄3 = 9.
    • If A + B = 70° and A + B + C = 180°,then 70° + C = 180°.
    • If X-Y-Z, then XY + YZ = XZ.
    • Let d be the distance between A and B.
warm up solutions
Warm-up Solutions
  • For each of these statements, name the postulate or theorem that justifies the statement:
    • If x + 1 = 2x, then 1 = x. The subtraction property
    • If x⁄3 – 6 = 3, then x⁄3 = 9. The addition property
    • If A + B = 70° and A + B + C = 180°,then 70° + C = 180°. The substitution property
    • If X-Y-Z, then XY + YZ = XZ.The Betweenness of Points Theorem
    • Let d be the distance between A and B.The Ruler Postulate
definitions
Definitions
  • Two angles are complementary iff their measures add up to 90°.
    • Each of these angles is the other’s complement.
  • Two angles are supplementary iff their measures add up to 180°.
    • Each of these is the other’s supplement.
new theorems
New Theorems
  • Complements of the same angle are of equal size.
  • Supplements of the same angle are of equal size.
theorem 3 proof
Theorem 3 – Proof

Given: 1 and 2 are complements of 3.

Prove: 1 = 2

Statement

Reason

  • 1 and 2 are complements of 3.
  • 1 + 3 = 90°2 + 3 = 90°
  • 1 + 3 = 2 + 3
  • 1 = 2
  • Given.
  • Definition of complementary.
  • Substitution.
  • Subtraction (– 3)
definitions1
Definitions
  • Opposite rays point in opposite directions and share the same endpoint.
    • In other words, they form a straight angle (180°).
  • Two angles form a linear pair iff they share a common side and their other sides are opposite rays.
  • Two angles are vertical angles iff the sides of one are opposite rays to the sides of the other.
theorems
Theorems
  • Theorem 5 (“Linear Pair Theorem”):
    • The angles in a linear pair are supplementary.
  • Theorem 6 (“Vertical Angles Theorem”):
    • Vertical angles are congruent.
homework
Homework
  • From Chapter, Section:
clean up reminders
Clean-up / Reminders
  • Pick up all trash / items.
  • Push in chairs (at front and back tables).
  • See you tomorrow!
practice quiz
Practice Quiz
  • When you are finished, put away your pencil and take out two pens/pencils of different color for corrections.
    • First color = careless mistakes / “I knew that!”
    • Second color = things not understood / “I should review this!”
  • Come to my desk to pick up a solutions sheet,and check your work.
  • When you’re done with the solutions sheet, bring it back to me.
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