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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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## PowerPoint Slideshow about 'GBK Geometry' - avani

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### GBK Geometry

Jordan Johnson

• Greeting

• Review Asg #17

• Practice Quiz

• Lesson:

• Homework / Questions

• Clean-up

• 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.

• 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

• 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.

• Complements of the same angle are of equal size.

• Supplements of the same angle are of equal size.

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)

• 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.

• Theorem 5 (“Linear Pair Theorem”):

• The angles in a linear pair are supplementary.

• Theorem 6 (“Vertical Angles Theorem”):

• Vertical angles are congruent.

• From Chapter, Section:

• Pick up all trash / items.

• Push in chairs (at front and back tables).

• See you tomorrow!

• 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.