Gbk geometry
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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

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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


Fields of vision

Fields of Vision


Popular mechanics 1902

Popular Mechanics1902


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)


German geometry

German geometry


German geometry1

German geometry


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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