Geometry

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# Geometry - PowerPoint PPT Presentation

Geometry. Chapter 1 Review Lessons 1.1 – 1.7 TEST Friday, October 25 Homework: Page 90 - 92/ 1 - 32, 35 – 44. Lesson 1.1 Building Blocks of Geometry. Point. A location in space. No size. Line. A set of collinear points having no endpoints. No width, only length.

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### Geometry

Chapter 1 Review

Lessons 1.1 – 1.7

TEST Friday, October 25

Homework:

Page 90 - 92/ 1 - 32, 35 – 44

Lesson 1.1 Building Blocks of Geometry

Point

A location in space. No size

Line

A set of collinear points having no endpoints. No width, only length.

A set of points that creates a flat surface that has no depth or edge. Length & width, no height.

Plane

Collinear

C

A

B

A set of points that lie on a line.

A •

Coplanar

A set of points, segments, lines,… that lie on a plane.

B •

A

B

A

X

Y

Lesson 1.1 Building Blocks of Geometry

A set of collinear points having two endpoints.

Line Segment

A

B

Congruent Segments

Two or more line segments that are congruent (same size & shape)

X

Y

Midpoint of a Segment

A point that divides/bisects a segment into two equal parts.

G

A

A

X

Y

Lesson 1.1 Building Blocks of Geometry

Midpoint of a Segment (formula)

x 1, y1

x 2, y2

B

Ray

H

R

A

A

S

X

X

T

B

B

Lesson 1.1 - Building Blocks of Geometry

Angle

The union of two noncollinear rays having a common endpoint.

< AXB

Congruent Angles

Two or more angles with the same measure

AXB  RST means that the measure of both angles are equal.

Lesson 1.1 - Building Blocks of Geometry

Angle of Reflection

The reflection of an angle will have the same measure from the reflected surface as the initial angle.

50o

Incoming angle

=

Outgoing angle

50o

Lesson 1.1 - Building Blocks of Geometry

An angle whose measure is equal 90 o.

Right Angle

Acute Angle

An angle whose measure is < 90 o.

Obtuse Angle

An angle whose measure is > 90 o.

Lesson 1.1 - Building Blocks of Geometry

Complimentary Angles

Two angles whose sum of measure equals 90°.

1 +  2 = 90°.

1

6

2

7

Two angles whose sum of measure equals 90°.

6 +  7 = 90°.

Two angles whose sum of measure equals 180°.

 4 +  5 = 180°.

Supplementary Angles

4

5

Lesson 1.1 - Building Blocks of Geometry

Vertical Angles

Opposite and congruent angles formed by the intersection of two lines.

 1 =  2

1

2

Linear Pair of Angles

 8 +  9 = 180.

8

9

Lesson 1.1 - Building Blocks of Geometry

Polygon

A closed plane figure formed by the connecting line segments endpoint to endpoint with each segment intersecting exactly two other segments.

A polygon having the fewest possible number of sides.

Triangle

n-gon

A polygon with n number of sides where n is equal to any positive integer.

Octagon

Triangle

n = 3

n = 8

Lesson 1.1 - Building Blocks of Geometry

Naming Polygons

n= 5

Pentagon

Hexagon

n= 6

Octagon

n= 8

A

B

C

F

E

D

AF & FE

Lesson 1.1 - Building Blocks of Geometry

Polygon Features

Consecutive angles

FAB & ABC

Consecutive sides

Consecutive vertices

F & E

A

B

F

C

E

D

Lesson 1.1 - Building Blocks of Geometry

Diagonal of a Polygon

A line segment that connects two nonconsecutive vertices of a polygon.

AC. AD, & AE are each diagonals of this polygon.

Lesson 1.1 - Building Blocks of Geometry

Groups of Polygons

A polygon with all sides equal in length.

Equilateral polygon

A polygon with all angles equal in measure.

Equiangular polygon

A polygon with all angles equal in measure and all sides equal in length.

Regular polygon

Lesson 1.1 - Building Blocks of Geometry

Groups of Polygons

Equilateral polygon

The rhombus has all sides congruent.

The rectangle has all angles congruent.

Equiangular polygon

The square has all angles and sides congruent.

Regular polygon

Lesson 1.1 - Building Blocks of Geometry

Right Triangle

A triangle with one right angle.

Acute Triangle

A triangle with three acute angles.

Lesson 1.1 - Building Blocks of Geometry

Obtuse Triangle

A triangle with one obtuse angle.

Scalene Triangle

A triangle with no congruent sides.

Lesson 1.1 - Building Blocks of Geometry

Equilateral Triangle

A triangle with all sides congruent.

Isosceles Triangle

A triangle with two congruent sides.

AB DC

A

B

AB DC

C

AC BD

D

Lesson 1.1 - Building Blocks of Geometry

Trapezoid

A quadrilateral with two sides parallel.

B

A

C

D

A quadrilateral with both pairs of opposites sides parallel and congruent.

Parallelogram

A

D

B

C

AB DC

AB  BC  CD  DA

Lesson 1.1 - Building Blocks of Geometry

Kite

A quadrilateral with opposite sides parallel and all sides congruent.

Rhombus

A

D

B

C

AB  DC

AB DC

AB DC

AB  BC  CD  DA

AC BD

Lesson 1.1 - Building Blocks of Geometry

Rectangle

A parallelogram with all angle congruent (right angles).

A

B

D

C

A parallelogram all angles congruent and all sides congruent.

Square

A

B

D

C

Lesson 1.1 - Building Blocks of Geometry
• Circle –The set of points equidistant to a given point.
• Radius – A segment with one endpoint on the circle and one endpoint on the center. XA
• Diameter – A chord that passes thru the center of the circle. EB
• Chord – A segment whose endpoints lie on the circle. FD
• Tangent – A line that intersects a circle at only one point. Line GC
• Arc – The distance between two points on a circle. AB

A

F

B

E

X

D

C

G

Conjectures

• Through any two points there is exactly one line.

A· ·B

• Through any three points there is at least one plane and through any three non-collinear points there is exactly one plane.

. A B .

. C

A

l

m

Conjectures

• If two lines intersect, then they intersect in exactly one point.

Line l intersects line m at A.

A

Y

X

B

Dimensions

• A line contains at least two points
• A plane contains at least 3 points not in a line
• Space contains at least four points not all in one plane

1 dimension

2 dimensions

3 dimensions