Geometry-Definitions, Postulates, Properties, & Theorem - PowerPoint Presentation

Slide1

Geometry-Definitions, Postulates, Properties, & Theorems

CH 3-Perpendicular & Parallel LinesGeometry ISlide2

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Navigating the PowerPointSlide3

Main Menu

Background Info

Postulates

Theorems

Theorems Cont.

Basic Definitions

Quiz

(end of class)

Quiz Info

(next day)

Quizlet

(HW)

Helppp

!!

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✪Slide4

A theorem is a statement that has been proven on previously established statements like other theorems and postulates.

A theorem is a proof of the truth of the resulting expression.A theorem is a logical argument in the sense that if a hypothesis is true then the conclusion must also be true.A postulate is a statement that is accepted without proof and is fundamental to a subject

Background InfoSlide5

NOTE: Click each theorem to take you to another slide with examples

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicularIf two sides of two adjacent acute angles are perpendicular, then the angles are complementary

If two lines are perpendicular, then they intersect to form four right angles

TheoremsSlide6

Alternate Interior Angles: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Consecutive Interior Angles: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementaryAlternate Exterior Angles

: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Theorems Cont.Slide7

Note: Click each postulate to go to another slide with examples

Parallel Postulate: If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given linePerpendicular Postulate

: If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line

Corresponding Angles Postulate

: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

PostulatesSlide8

NOTE: Click each definition to be directed to another slide with examples

Parallel Lines-Two lines that are coplanar and do not intersectSkew Lines- Two lines that do not intersect and are not coplanar

Transversal

- A line that intersects two or more coplanar lines at different points

Perpendicular Lines

- Two lines intersect to form a right angleBasic DefinitionsSlide9

Homework (Print off a copy to bring to class) Go to quizlet.com

Select create in the upper left-hand cornerMake flashcardsCreate an accountView the extra featuresStudy your flashcards for the quiz tomorrow

QuizletSlide10

Out of the 13 definitions only 5 will be on the quiz tomorrow. A mixture of the names and definitions will be placed in a cup. From there, you and your classmates will come to the front and choose one from the cup. If the name or part of the definition is drawn, the definition must be written (Pretty close to word-for-word). If the definition is drawn, the name must be written. After the 5, students can raise their hands if they wish to continue with the quiz. It only takes 1 to force the class to answer more.

Quiz InfoSlide11

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✪Slide12

This slide explains the definitions of theorems and postulates.

BI (Background Info)Slide13

The first three of the chapter are given along with their definitions. Click the postulate to take you to another slide where examples are presented.

P (Postulates)Slide14

The first six theorems of the chapter are given along with their definitions. Click the theorem to take you to another slide where examples are presented.

T (Theorems)Slide15

This slide is a continuation of the previous theorems slide.

TC (Theorems Cont.)Slide16

Four definitions are given. Buttons take you to another slide where visuals are displayed.

BD (Basic Definitions)Slide17

This slides provides a link to take you to the end of the presentation where there will be a short quiz. The quiz will not be graded, but try your best because it is great practice for the quiz tomorrow!

Q (Quiz)Slide18

This slide provides information on and the expectations for the quiz the following day.

QI (Quiz Info)Slide19

This slide provides a brief explanation on how to use Quizlet and what is expected for the homework for the following day.

Qui-zlet (Quizlet

)Slide20

This slide presents ways to get extra assistance if needed. It also provides buttons for each of the sections, which take you to another slide that describes each of the sections.

The titles of the buttons are abbreviated by the first letter of each word.H (

Helppp

!!)Slide21

This theorem is quite significant in geometry. We will use it during proofs. Click the picture below to see an example of a proof that we will use this theorem for.

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular

Click

Theorem

to return

to TheoremsSlide22

Below is a link to a video of a proof that we will solve in this class

Video Proof

If two sides of two adjacent acute angles are perpendicular, then the angles are complementary

Click

Theorem

To return to

TheoremsSlide23

Using this theorem and the definitions of perpendicular lines and right angles, you will be able to write different kinds of proofs for the same situation.

If two lines are perpendicular, then they intersect to form four right angles

Proof Hints:

Use definition of perpendicular lines to find one right angle.

Use vertical and linear pairs of angles to find three more right angles.

Click

Theorem

to return to TheoremsSlide24

Click on the link below to watch a video on the proof of the theorem.AIA

Alternate Interior Angles: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Click

TC

to return to Theorems Cont.Slide25

Click on the link to watch a video on a proofCIA

Consecutive Interior Angles: If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary

Click

TC

to return to Theorems Cont.Slide26

Alternate Exterior Angles: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent

Click

TC

to return to Theorems Cont.Slide27

Parallel Postulate: If there is a line and a point not on the line, then there is exactly one line through the point parallel to the given line

Click

P

ostulate

to return to PostulatesSlide28

Perpendicular Postulate: If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line

If we wanted to measure the

distance between

a point and a line, we can employ the Perpendicular Postulate, a compass, and a straightedge, since there exists only one perpendicular line from a point to a line

. Click the button below for an example:

Click

Postulate

to

return to PostulatesSlide29

So, in the figure below, if l || m, then

angle 1 is congruent to angle 2.Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Click

Postulate

to return to PostulatesSlide30

Parallel Lines-Two lines that are coplanar and do not intersect

Click this button!!!

Click

BD

to return to Basic Definitions.Slide31

Skew Lines- Two lines that do not intersect and are not coplanar

Click

BD

to return to Basic DefinitionsSlide32

Transversal- A line that intersects two or more coplanar lines at different points

Click

BD

to return to Basic DefinitionsSlide33

Perpendicular Lines- Two lines intersect to form a right angle

Click the button!!

Click

BD

to return to Basic DefinitionsSlide34

Click this button to return to the theoremSlide35

The next few slides are a short quiz that will not be graded, but it is great practice for tomorrow’s quiz!This quiz is meant to be completed after you have gone through the full PowerPoint.

You must answer the questions correctly before moving on to the next questionClick the Start button to begin

StartSlide36

True or False: This is the correct definition of parallel lines:

Two lines are parallel if and only if they do not intersect.Click True or False True

False

Question 1Slide37

Return to ?

Move to next ?Slide38

Return to the ?

*Hint:

There is a key word missing from the definition.

Think about the definition of skew lines and how the two differ.Slide39

True or False:A postulate is a statement that is accepted without proof and is fundamental to a subject

TrueFalse

Question 2Slide40

Next ?

Return to the ?Slide41

Return to the ?

*Hint:

You’ll find the answer on the Background Info slideSlide42

Fill in the blank:If two sides of two adjacent acute angles are perpendicular, then the angles are ________

ComplementarySupplementary

Obtuse

Question 3Slide43

Next ?

Return to the ?Slide44

Return to the ?

*Hint:

Refer to the

Theorems slideSlide45

Which can you add to the blanks to make the statement correct?

If two parallel lines are cut by a transversal, then the pairs of _____ _____ angles are congruent.Consecutive InteriorAlternate Exterior

Alternate Interior

I. and II.

II. and III.

All three

Question 4Slide46

Next ?

Return to the ?Slide47

Return to the ?

*Hint:

Check out the

theorems Slide48

What makes the following statement incorrect?A theorem is a statement that hasn’t

been proven on previously established statements like other theorems and postulates.Proven

Statements

Hasn’t

Question 5Slide49

End

Return to the ?Slide50

Return to the ?

*Hint:

Is a theorem a

p

roven statement?Slide51

You have completed the lesson! Remember to study for your quiz! Slide52

ReferencesSlide53

References Cont.Slide54

References Cont.Slide55

References Cont.