# INCENTER CIRCUMCENTER ORTHOCENTER AND CENTROID OF A TRIANGLE PDF

The centroid of a triangle is constructed by taking any given triangle and connecting the midpoints of each leg of the triangle to the opposite vertex. The line segment created by connecting these points is called the median. You see the three medians as the dashed lines in the figure below. No matter what shape your triangle is, the centroid will always be inside the triangle. You can look at the above example of an acute triangle, or the below examples of an obtuse triangle and a right triangle to see that this is the case.

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The orthocenter is the point of intersection of the three heights of a triangle. A height is each of the perpendicular lines drawn from one vertex to the opposite side or its extension. The centroid is the point of intersection of the three medians. A median is each of the straight lines that joins the midpoint of a side with the opposite vertex.

The centroid divides each median into two segments , the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side. The circumcenter is the point of intersection of the three perpendicular bisectors.

A perpendicular bisectors of a triangle is each line drawn perpendicularly from its midpoint. The circumcenter is the center of a triangle's circumcircle circumscribed circle. The incenter is the point of intersection of the three angle bisectors.

The angle bisectors of a triangle are each one of the lines that divide an angle into two equal angles. The incenter is the center of the circle inscribed in the triangle. The orthocenter , the centroid and the circumcenter of a non-equilateral triangle are aligned ; that is to say, they belong to the same straight line, called line of Euler. I am passionate about travelling and currently live and work in Paris.

I like to spend my time reading, gardening, running, learning languages and exploring new places. Download it in pdf format by simply entering your e-mail! Orthocenter, Centroid, Circumcenter and Incenter of a Triangle. Learn from home The teachers.

Orthocenter The orthocenter is the point of intersection of the three heights of a triangle. Daniella 7 reviews 1st lesson free! Mark 5 reviews 1st lesson free! Sandra 1 review 1st lesson free! Alex 3 reviews 1st lesson free! Dr parikh 8 reviews 1st lesson free! Naomi 7 reviews 1st lesson free! Myriam 13 reviews 1st lesson free! Intasar 10 reviews 1st lesson free!

Did you like the article? Superprof 5 votes, average: 4. Did you like this resource? This comment form is under antispam protection. Notify of. Theory Angle Bisectors. Angles of a Polygon. Angles of the Triangle. Area and Perimeter of Polygons. Area and Perimeter of a Triangle. Circular Sectors. Circular Segments. Circumscribed Polygons. Concentric Circles.

Diagonals of a Polygon. Equilateral Triangles. Height of a Polygon. Regular Hexagons. Inscribed Polygons. Irregular Polygons. Line Segments. Lune of Hippocrates. Medians of a Triangle. Regular Pentagons. Perpendicular Bisectors. Plane Equation. Points, Lines and Planes. Quadrilaterals and Regular Polygons. Regular Polygons. Right Triangle.

Sheaf of Planes. Sides of a Polygon. Similar Triangles. Star Polygons. Intersection of Three Planes. Intersection of Two Planes. Area Formulas. Area and Perimeter Formulas. Circle Formulas. Geometry Formulas. Perimeter Formulas.

Plane Formulas. Triangle Formulas. Area Word Problems. Area Worksheet. Circle Word Problems. Circle Worksheet. Plane Problems. Pythagorean Theorem Word Problems. Pythagorean Theorem. Pythagorean Theorem Worksheet. Rectangle Problems. Square Problems. Trapezoid Problems. Triangle Problems.

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## Triangle Centers

Math [ Privacy Policy ] [ Terms of Use ]. If you would explain to me, I would be most grateful! The orthocenter is the intersection of the triangle's altitudes. The circumcenter is the center of the circumscribed circle the intersection of the perpendicular bisectors of the three sides. The centroid is the intersection of the three medians of the triangle. There's also the incenter, which is the intersection of the angle bisectors of the triangle.

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## Orthocenter, Centroid, Circumcenter and Incenter of a Triangle

For each of those, the "center" is where special lines cross, so it all depends on those lines! Draw a line called a "median" from each corner to the midpoint of the opposite side. Where all three lines intersect is the centroid , which is also the "center of mass":. Try this: cut a triangle from cardboard, draw the medians. Do they all meet at one point? Can you balance the triangle at that point? Try this: drag the points above until you get a right triangle just by eye is OK.

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## Various Triangle Centers

This page requires a java-enabled browser for correct functioning. The bright red points A, B, and C can be moved around with the mouse and the figure will adjust accordingly. The centroid of a triangle is the point at which the three medians meet. A median is the line between a vertex and the midpoint of the opposite side.

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## How to Find the Incenter, Circumcenter, and Orthocenter of a Triangle

The orthocenter is the point of intersection of the three heights of a triangle. A height is each of the perpendicular lines drawn from one vertex to the opposite side or its extension. The centroid is the point of intersection of the three medians. A median is each of the straight lines that joins the midpoint of a side with the opposite vertex. The centroid divides each median into two segments , the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side. The circumcenter is the point of intersection of the three perpendicular bisectors.