Since LM = AM, point M must be on the perpendicular bisector of AL. Since AM = BM, BL must be perpendicular to AL. This makes ∆ALC a right triangle with hypotenuse AC twice the length of side AL. Hence ∠LAC = ∠LAB = 60°, and AL is angle bisector, median, and altitude.
ΔABC is isosceles with ∠A = 120°, and ∠B = ∠C = 30°.
A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
<h3>What is a line segment?</h3>A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.
<h3>What is a perpendicular bisector?</h3>A perpendicular bisector can be defined as a type of line that bisects (divides) a line segment exactly into two (2) halves and forms an angle of 90 degrees at the point of intersection.
In this scenario, we can reasonably infer that to divide the triangles into these regions, you should construct the <u>perpendicular bisector</u> of each segment. These perpendicular bisectors intersect and divide each triangle into three regions. The points in each region are those closest to the vertex in that <u>region</u>.
Read more on perpendicular bisectors here: brainly.com/question/27948960
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