GBK Geometry

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# GBK Geometry - PowerPoint PPT Presentation

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

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 = 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
• 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
• 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
• Complements of the same angle are of equal size.
• Supplements of the same angle are of equal size.
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)
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
• Theorem 5 (“Linear Pair Theorem”):
• The angles in a linear pair are supplementary.
• Theorem 6 (“Vertical Angles Theorem”):
• Vertical angles are congruent.
Homework
• From Chapter, Section:
Clean-up / Reminders
• Pick up all trash / items.
• Push in chairs (at front and back tables).
• See you tomorrow!
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.