**Welcome to Chapter 3: Using Tools of Geometry**

3.8 The Centroid

Vocabulary:

Centroid: The point of concurrency of the three medians and the center of gravity of a triangle

C-14 Median Concurrency Conjecture: The medians of a triangle are ______.

C-15 Centroid Conjecture: The centroid of a triangle divides each median into two parts so that the distance from the centroid to the vertex is _______ the distance from the centroid to the midpoint of the opposite side.

C-16 Center of Gravity Conjecture: The ______ of a triangle is the center of gravity of the triangular region.

3.1 Duplicating Segments and Angles

Vocabulary:

Sketch: freehand drawing using only a pencil

Draw: careful and accurate drawing using only a pencil and ruler

Construct: precise drawing using only a compass and straightedge

C-5 Perpendicular Bisector Conjecture: If a point is on the perpendicular bisector of a segment, then it is ________ from the endpoints of the segment.

C-6 Converse of the Perpendicular Bisector Conjecture:

If a point is equidistant from the endpoints of a segment, then it is on the _________ of the segment.

3.2 Constructing Perpendicular Bisectors

Vocabulary:

Segment Bisector: a line, ray or segment in a plane that passes through the midpoint of a segment in a plane.

Perpendicular Bisector: a line segment that bisects a line at a 90 degree angle.

Coincide: line or line segments that are identical to each other

Median: line segment connecting the vertex of a triangle to the mid point of the opposite side

Mid-segment: a line segment connecting the midpoints of two sides of a triangle

C-7 Shortest Distance Conjecture: The shortest distance from a point to a line is measured along the _______ segment from the point to the line.

**Bibliography:**

Website: .khanacademy.org

Website: .youtube.com

Book: Discovering Geometry An Investigative Approach

Book: History's 100 Greatest

Events

Website: .khanacademy.org

Website: .youtube.com

Book: Discovering Geometry An Investigative Approach

Book: History's 100 Greatest

Events

3.3 Constructing Perpendiculars to a Line

Constructing Angles by Parallel Lines

Formation of Parallel Lines

More Parallel Lines...

By: Amanda

& Gabriel Lipari

3.5 Constructing Parallel Lines

3.6 Constructing Problems

Distance from a point to a line: length

of the perpendicular sector to the line

Altitude: perpendicular segment from

a vertex to the opposite side or to a line

containing the opposite side

C-8 Angle Bisector Conjecture: If a point is on the bisector of an angle, then it is ________ from the sides of the angle.

This house is made up of what 2-D shapes?

(Hint: Be specific)

Vocabulary:

Angle Bisector: a line segment or ray that divides an angle into congruent angles

Vocabulary:

Determine: to decide or conclude after reasoning

Incenter

Circumcenter

Orthocenter

Vocabulary:

Parallel lines: Lines that lie in the same plane and do not intersect

C-9 Angle Bisector Concurrency Conjecture: The three angle bisectors of a triangle are _______.

C-10 Perpendicular Bisector Concurrency Conjecture: The perpendicular bisectors of a triangle are _______.

C-11 Altitude Concurrency Conjecture: The three altitudes or line containing the altitudes of a triangle are _______.

C-12 Circumcenter Conjecture: The circumcenter of a triangle is _______ from the _______.

C-13 Incenter Conjecture: The incenter of a triangle is _______ from the ______.

An _____ is a polygon with 8 sides.

Trivia Question:

The Centroid is where the three ______ of triangle intersect at a point of concurrency.

When you

sketch

a triangle, you make a _______ drawing.

When you

draw

a triangle, you accurately draw it with a ______ and _____.

When you

construct

a triangle, you precisely draw it with a _____ and ______.

**Welcome to**

Geometric City

Geometric City

Fill in the Blank...

The Nine-Point Circle consists of the

incenter, circumcenter,

and

orthocenter

of a triangle.

Welcome to Rectangular Village

Nine-Point Circle

3.7 Constructing Points of Concurrency

Vocabulary:

Incenter: The point of concurrency of the three angle bisectors in a triangle

Circumcenter: The point of concurrency of the three perpendicular bisectors in a triangle

Orthocenter: The point of concurrency of the three altitudes in at triangle

Conjectures #9-13

Perpendicular Bridge

Trivia Question:

The formula for the circumference and area for the wheels of this bike are _______ and ________.

What is the shape of this sign?

(Hint: Be specific)

**What kind of 3-D shapes can you see?**

Duplication of Segments and Angles:

To use a protractor and ruler: _______.

To use a compass and straightedge: _______.

Construction of Perpendicular Lines:

When a perpendicular segment bisects a line, it creates a ______ angle.

The Points of Concurrency:

The ______ is the point of concurrency equidistant from the sides of a triangle.

The point of concurrency equidistant from the three vertices of a triangle is ______.

**Quiz Questions**