Which Line Segments 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. Information technology works past amalgam the perpendicular bisectors of any ii sides to discover their midpoints. Then the medians are drawn, which intersect at the centroid. This structure assumes you lot are already familiar with Amalgam the Perpendicular Bisector of a Line Segment.

Printable stride-by-pace instructions

The above animation is available as a printable step-past-step educational activity sheet, which can be used for making handouts or when a computer is non available.

Proof

The image below is the final drawing from the higher up blitheness.

	Argument	Reason
1	S is the midpoint of PQ	S was found by constructing the perpendicular bisector of PQ. See 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. See Median of a triangle.
3	Similarly, PT is a median of the triangle PQR	Every bit in (1), (2).
4	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.Due east.D

Attempt it yourself

Click hither for a printable worksheet containing centroid construction issues. When y'all get to the folio, utilise the browser print command to impress 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 point on a line
Perpendicular from a line through a point
Perpendicular from endpoint of a ray
Divide a segment into n equal parts
Parallel line through a indicate (bending re-create)
Parallel line through a indicate (rhombus)
Parallel line through a betoken (translation)

Angles

Bisecting an bending
Copy an angle
Construct a 30° angle
Construct a 45° angle
Construct a 60° angle
Construct a 90° angle (right angle)
Sum of n angles
Departure of 2 angles
Supplementary angle
Complementary bending
Constructing 75° 105° 120° 135° 150° angles and more

Triangles

Re-create a triangle
Isosceles triangle, given base and side
Isosceles triangle, given base and distance
Isosceles triangle, given leg and apex angle
Equilateral triangle
30-60-90 triangle, given the hypotenuse
Triangle, given 3 sides (sss)
Triangle, given one side and side by side angles (asa)
Triangle, given two angles and not-included side (aas)
Triangle, given two sides and included bending (sas)
Triangle medians
Triangle midsegment
Triangle distance
Triangle distance (outside example)

Right triangles

Right Triangle, given i leg and hypotenuse (HL)
Correct Triangle, given both legs (LL)
Correct Triangle, given hypotenuse and one angle (HA)
Right Triangle, given i 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 point 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 i side
Square inscribed in a circle
Hexagon given one side
Hexagon inscribed in a given circumvolve
Pentagon inscribed in a given circumvolve

Non-Euclidean constructions

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

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

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