Point A is a midpoint and Point B is the centroid of the triangle pictured below, if the length of BC is 12, what is the length of AB ? The Centroid of a Triangle is the center of mass of that Triangle Theorem 5.8 Concurrency of Triangle Medians The Medians of a Triangle intersect at a point that is two thirds ( 𝟐 𝟑 ) of the distance from each vertex to the midpoint of the opposite side. Triangle RQT has median QS Triangle TQR has median RS Triangle SQR has median ST Do this for all three sides and find the centroid of the triangleĦ Human Medians Triangle RST has median TQ Triangle RSQ has median RT Draw a segment from that midpoint to the opposite vertex. Use a straightedge to find the midpoint of the side.
#Whats a median geometry download#
Download Notes at: goo.gl/Or0UZhĤ Median of a Triangle A median of a triangle is a line segment that joins the vertex of a triangle to the midpoint of the opposite side. Main Idea: Identify and Use the Centroid and Orthocenter of a Triangle to solve problems. QU is an angle bisector of Δ QRS because it bisects ∠ RQS.1 Refresher Questions What is a Median of a Triangle?Ģ Section 5.4 Medians, Altitudes and Triangles SP is a median to base QR because P is the midpoint of QR. RT is an altitude to base QS because RT ⊥ QS. In Figure, the altitude drawn from the vertex angle of an isosceles triangle can be proven to be a median as well as an angle bisector.įigure 9 The altitude drawn from the vertex angle of an isosceles triangle.Įxample 1: Based on the markings in Figure 10, name an altitude of Δ QRS, name a median of Δ QRS, and name an angle bisector of Δ QRS.įigure 10 Finding an altitude, a median, and an angle bisector.
In certain triangles, though, they can be the same segments.
In general, altitudes, medians, and angle bisectors are different segments. In every triangle, the three angle bisectors meet in one point inside the triangle (Figure 8).įigure 8 The three angle bisectors meet in a single point inside the triangle. In Figure, is an angle bisector in Δ ABC.
Every triangle has three angle bisectors. In every triangle, the three medians meet in one point inside the triangle (Figure 6).įigure 6 The three medians meet in a single point inside the triangle.Īn angle bisector in a triangle is a segment drawn from a vertex that bisects (cuts in half) that vertex angle. Which may or may not be inside the triangle.Ī median in a triangle is the line segment drawn from a vertex to the midpoint of its opposite side. It is interesting to note that in any triangle, the three lines containing the altitudes meet in one point (Figure 4).įigure 4 The three lines containing the altitudes intersect in a single point, įigure 3 An altitude for an obtuse triangle. In Figure 3, AM is the altitude to base BC. įigure 2 In a right triangle, each leg can serve as an altitude. In Figure 2, AC is an altitude to base BC, and BC is an altitude to base AC. Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side) (Figure 1).įigure 1 Three bases and three altitudes for the same triangle.Īltitudes can sometimes coincide with a side of the triangle or can sometimes meet an extended base outside the triangle. Now isn't that kind of special?Įvery triangle has three bases (any of its sides) and three altitudes (heights). Just as there are special names for special types of triangles, so there are special names for special line segments within triangles.
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