drill. angles * an angle is made up of two rays that share the same endpoint. to name an angle we...

DRILLDRILL

AnglesAngles* An angle is made up of two rays that share

the same endpoint.

ABC

•To name an angle we either can use the one point where the vertex is located if there is only one angle, otherwise we must use three points making sure the vertex is in the middle.

A

CB

B

Naming Angles

ED

A C B

1.4 Measuring Angles

& Segments

Notes(Vocab)Ruler Postulate: the distance

between any two points is the absolute value of the difference.

Congruent: Is the term used in Geometry to describe two shapes or objects which are Equal.

Segment Addition Postulate:

If three points A, B, and C are collinear and B is between A and C, then AB + BC =AC.

A CB

Measuring Angles: an angle measure is found by taking the absolute value of the difference of each angle.

Angle Addition Postulate: If two angles share a common ray then the sum of those two angles is equal to the larger angle.

A D

BC

DrillDrill1) Draw a segment so that A and C are

the endpoints and B is somewhere between them.

2) If AB is 10 feet and BC is 18 feet, how long is AC?

3) If AB is 2x feet and BC is 3x + 4 feet and AC is 39 feet how long is AB?

1.5 Good Definitions

What is a Polyglob?

Properties of Good Definitions• Uses clearly understood terms,

meaning they should be commonly understood or previously defined.

• Is Precise, Avoid words such as large, sort of, and some.

• States what the term is, rather then what it is not.

Ex: Big is the opposite of small.

Midpoint:Midpoint: is the point that divides a segment into two congruent parts.

Perpendicular Lines:Perpendicular Lines: are lines that intersect to make a right angle.

Perpendicular Bisector:Perpendicular Bisector: is a perpendicular line that passes through the mid point of a segment.

Angle Bisector:Angle Bisector: is a ray that divides an angle into two congruent parts.

DrillDrill

1) A B CIf AB is 15 and AC is 80 find BC.

2) Is this a good definition? Explain

An apple is a fruit that is not an orange.

3) 30, 26, 21, 15, ___, ___, ___

A B CIf AB is 15 and AC is 80 find BC.

80 – 15 = 65 therefore BC = 6580 – 15 = 65 therefore BC = 65

An apple is a fruit that is not an orange.

No, b/c of the word NOT being used.No, b/c of the word NOT being used.

3) 30, 26, 21, 15, 88, , 00, , -9-9

1.6 Basic Constructions

Objective: The students will be able to construct perpendicular bisectors and angle bisectors, as well as understand their properties.

Tools For Constructions• Compass

• Straightedge

• Patty Paper

• Geometer’s Sketchpad

Perpendicular BisectorPerpendicular Bisector• Is a line that is perpendicular to a segment

and passes through the midpoint.

Steps for Construction/Patty PaperSteps for Construction/Patty Papera) Trace the segment on the patty paper.b) Label Endpointsc) Fold paper so that the two endpoints match

up and unfold.d) Trace the fold to create your perpendicular

bisector

A B

Fold

M

Angle BisectorAngle Bisector• Is a ray that cuts an angle into two congruent

angles.

Steps for Construction/Patty PaperSteps for Construction/Patty Papera) Trace the angle on the patty paperb) Label Pointsc) Pinch the vertex and fold the paper so that

the two rays that create the angle match up and unfold

d) Trace the fold to create your angle bisector

A B

Fold

D

C

E

Summary• Constructed Perpendicular and Angle Bisectors

• Found measures using both types of bisectors

• Creating angle bisectors will lead us into vertical angles as well as linear angles.

DrillDrill1) A B CIf AB is 3x and BC is 2x + 10, find BC if AC equals 80 feet.

2) Does the ceiling and your desktop represent parallel planes? (WHY)

3) How many and what type of points do we need to name a plane?

1.7 Using Deductive Reasoning

Types of AnglesVertical AnglesVertical Angles

Vertical Angles are angles that are opposite each other where two lines intersect.

Ex : 1 & 3 as well as 2 & 4

Types of Angles

Adjacent AnglesAdjacent Angles

Adjacent Angles are angles that share a common endpoint and share a common ray.

Ex : Angles A and B

Types of Angles

Complementary AnglesComplementary Angles

Two angles that have a sum of 90 degrees.

Types of Angles

Supplementary AnglesSupplementary Angles

Two angles that have a sum of 180 degrees.

Guided PracticeGuided Practice

Guided PracticeGuided Practice

Guided PracticeGuided Practice

Homework

Worksheet # 1.7

1.8 The Coordinate Plane

FormulasThe Distance FormulaThe Distance Formula

212

212 )()( yyxxd

Midpoint Formula

2,

22121 yyxx