Basic Constructions and Points of Concurrency. Objectives. What is construction? Who invented this tool commonly used in geometry? Circumcenter Incenter Centroid Orthocenter Euler Line. TOOLS NEEDED. COMPASS STRAIGHT EDGE PENCIL PAPER YOUR BRAIN (THE MOST IMPORTANT TOOL).
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
Straightedge
Euclid, the ancient Greek mathematician is the acknowledged inventor of geometry.
He did this over 2000 years ago, and his book "Elements" is still regarded as the ultimate geometry reference.
Father of GeometryWhen two lines intersect at one point, we say that the lines
are intersecting. The point at which they intersect is
the point of intersection.
(nothing new right?)
Well, if three or more lines intersect at a common point, we say that the lines are concurrent lines.The point at which these lines intersect is called the point of concurrency.
Both sides are congruent make sure you see this or it is NOT a perpendicular bisector
Perpendicular Bisector
midpoint and perpendicular
A
A
A
A
A
B
B
B
B
B






MedianAltitudeNone Angle Perp
Bisector Bisector
A perpendicular bisector cuts a line exactly in half at a right angle.
The point where the 3 perpendicular bisectors meet is called the circumcentre.
The circle which passes through the vertices of the triangle with the circumcentre as its centre, is called the circumcircle.
yo
yo
xo
zo
xo
xo
zo
xo
The bisectors of the angles of a triangle are concurrent and the point of intersection is the centre of an inscribed circle.
An angle bisector is a line that cuts an angle exactly in half.
The point where the 3 medians meet is called the centroid.
A median of a triangle is a line from a vertex to the midpoint of the opposite side.
The point where the 3 altitudes meet is called the orthocenter.
An altitude of a triangle is a line from a vertex perpendicular to the opposite side.
The orthocenter, circumcenter, and the centroid are COLLINEAR in EVERY triangle!
Concurrent Lines
3 or more lines that intersect at a common point
Point of Concurrency
The point of intersection when 3 or more lines intersect.
Type of Line SegmentsPoint of Concurrency
Perpendicular Bisectors Circumcenter
Angle Bisectors Incenter
Median Centroid
Altitude Orthocenter
Points of Concurrency (con’t)
Points of Concurrency (con’t)