Which Line Segment Of A Triangle Do You Draw To Find The Centroid Of A Triangle

Centroid of a Triangle

This page shows how to construct the centroid of a triangle with compass and straightedge or ruler. The centroid of a triangle is the point where its medians intersect. It works past amalgam the perpendicular bisectors of whatever two sides to observe their midpoints. And so the medians are drawn, which intersect at the centroid. This construction assumes you are already familiar with Amalgam the Perpendicular Bisector of a Line Segment.

Printable step-by-step instructions

The above animation is available as a printable step-by-pace pedagogy sheet, which can be used for making handouts or when a computer is not available.

Proof

The epitome below is the final drawing from the above animation.

	Argument	Reason
1	S is the midpoint of PQ	S was found by constructing the perpendicular bisector of PQ. Meet Constructing the perpendicular bisector of a segment for the method and proof
2	RS is a median of the triangle PQR	A median is a line from a vertex to the midpoint of the opposite side. Meet Median of a triangle.
three	Similarly, PT is a median of the triangle PQR	Every bit in (1), (ii).
iv	C is the centroid of the triangle PQR	The centroid of a triangle is the point where its medians intersect. See Centroid of a triangle.

- Q.E.D

Effort it yourself

Click hither for a printable worksheet containing centroid construction problems. When you get to the page, employ the browser print control to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site

List of printable constructions worksheets

Lines

Introduction to constructions
Copy a line segment
Sum of n line segments
Difference of two line segments
Perpendicular bisector of a line segment
Perpendicular at a betoken on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Separate a segment into north equal parts
Parallel line through a point (angle copy)
Parallel line through a point (rhomb)
Parallel line through a signal (translation)

Angles

Bisecting an bending
Copy an bending
Construct a 30° bending
Construct a 45° bending
Construct a 60° angle
Construct a xc° angle (correct angle)
Sum of northward angles
Deviation of two angles
Supplementary bending
Complementary angle
Amalgam 75° 105° 120° 135° 150° angles and more than

Triangles

Copy a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and altitude
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-sixty-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given i side and adjacent angles (asa)
Triangle, given ii angles and non-included side (aas)
Triangle, given 2 sides and included bending (sas)
Triangle medians
Triangle midsegment
Triangle altitude
Triangle distance (outside instance)

Correct triangles

Right Triangle, given i leg and hypotenuse (HL)
Right Triangle, given both legs (LL)
Correct Triangle, given hypotenuse and ane angle (HA)
Correct Triangle, given ane leg and one angle (LA)

Triangle Centers

Triangle incenter
Triangle circumcenter
Triangle orthocenter
Triangle centroid

Circles, Arcs and Ellipses

Finding the center of a circle
Circle given 3 points
Tangent at a bespeak on the circumvolve
Tangents through an external point
Tangents to two circles (external)
Tangents to two circles (internal)
Incircle of a triangle
Focus points of a given ellipse
Circumcircle of a triangle

Polygons

Square given one side
Square inscribed in a circle
Hexagon given 1 side
Hexagon inscribed in a given circumvolve
Pentagon inscribed in a given circle

Non-Euclidean constructions

Construct an ellipse with string and pins
Find the eye of a circle with any correct-angled object

Source: https://www.mathopenref.com/constcentroid.html

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