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Chapter 2: Problem 20

Draw a scalene acute triangle and construct its three medians. Label the centroid.

Short Answer

Expert verified
Draw a scalene acute triangle, identify midpoints, draw medians from vertices to opposite midpoints, and label the centroid where medians intersect.

Step by step solution

01

Draw a Scalene Acute Triangle

Start by drawing a triangle where all sides have different lengths and all angles are less than 90 degrees. Ensure none of the sides are equal and none of the angles are 90 degrees.
02

Identify the Midpoints

Find and mark the midpoints of each side of the triangle. These points will be used to draw the medians.
03

Draw the Medians

From each vertex of the triangle, draw a line to the midpoint of the opposite side. These lines are the medians of the triangle.
04

Label the Centroid

The point where all three medians intersect is known as the centroid. Clearly label this point as the centroid on your drawing.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

medians of a triangle
Medians are essential segments in a triangle. A median connects a vertex to the midpoint of the opposite side. In every triangle, there are three medians. These medians help in dividing the triangle into smaller triangles of equal area. To draw a median, start from any vertex and draw a line to the midpoint of the opposite side. Repeat this for all vertices. Using medians, you can understand balance and symmetry within the triangle.
centroid
The centroid is a significant point inside a triangle. It is where all three medians meet or intersect. This point is crucial because it serves as the triangle's center of gravity or balance point. The centroid has an interesting property: it divides each median into two segments with a ratio of 2:1, with the longer segment always being closer to the vertex. To locate the centroid, draw all three medians of the triangle, and mark the point where they intersect.
midpoints
Midpoints are the points that lie exactly halfway along the sides of a triangle. To find a midpoint, measure the length of a triangle's side and place a point at half that distance. Midpoints are crucial for constructing medians as they represent the ends of these segments on a side, opposite a vertex. Ensure you accurately measure and mark these points to draw precise medians and locate the centroid correctly.

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Most popular questions from this chapter

Given: \(\mathrm{Cis}\) the midpoint of \(\overline{A E}\) and of \(\overline{B D}, \overline{A B} \perp \overline{B D},\) and \(\overline{D E} \perp \overline{B D}\) Prove: \(\triangle A B C \cong \triangle E D C\)

Draw a scalene obtuse triangle and construct its three angle bisectors. Label the incenter.

Will the centroid of a triangle always be inside the triangle? Explain.

Construct a right isosceles triangle with legs that are about 2 inches in length.

Draw a scalene obtuse triangle and construct its three altitudes. Label the orthocenter.
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