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The Road of Geometry
Transcript of The Road of Geometry
Welcome to Chapter 3: Using Tools of Geometry
3.8 The Centroid
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
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
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.
Book: Discovering Geometry An Investigative Approach
Book: History's 100 Greatest
3.3 Constructing Perpendiculars to a Line
Constructing Angles by Parallel Lines
Formation of Parallel Lines
More Parallel Lines...
& 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)
Angle Bisector: a line segment or ray that divides an angle into congruent angles
Determine: to decide or conclude after reasoning
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.
The Centroid is where the three ______ of triangle intersect at a point of concurrency.
a triangle, you make a _______ drawing.
a triangle, you accurately draw it with a ______ and _____.
a triangle, you precisely draw it with a _____ and ______.
Fill in the Blank...
The Nine-Point Circle consists of the
of a triangle.
Welcome to Rectangular Village
3.7 Constructing Points of Concurrency
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
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 ______.