Special Segments and Sectors of Triangles

Special Segments of Triangles

​Connects a vertex of a triangle with the midpoint on the opposite side. Every triangle has 3 medians.

​Median

Math Response

In the diagram, TK is a median. Find KS if RS=14

Type answer here

Correct Answer: 7

Deg^°

Rad

Math Response

In the diagram, QS and RT are medians. If $$PT=3x-1$$ , $$PS=4x-2$$ , and $$SR=2x+4$$ . Find TQ

Type answer here

Correct Answer: 8

Deg^°

Rad

Math Response

Find DC if $$DC=x+5$$ and $$HC=x-3$$

Type answer here

Correct Answer: 16

Deg^°

Rad

​a segment that is perpendicular to a side of a triangle, and it intersects the vertex of the opposite side.

​Altitude

Math Response

In the isosceles triangle, PN is an altitude and $$m\angle M=40\degree$$ , find $$m\angle MPN$$

Type answer here

Correct Answer: 30

Deg^°

Rad

Math Response

AC is an altitude of the triangle. Find $$m\angle1$$ . The $$m\angle CAD=50\degree$$

Type answer here

Correct Answer: 120

Deg^°

Rad

Math Response

Find x. AD is an altitude of triangle ABC

Type answer here

Correct Answer: 24

Deg^°

Rad

A special segment of a triangle that bisects the angle of the triangle and intersects the opposite side of the triangle.

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Angle Bisector

Math Response

MK is an angle bisector. If $$m\angle2=50\degree$$ , what is $$m\angle1$$ ?

Type answer here

Correct Answer: 50

Deg^°

Rad

Math Response

MK is an angle bisector, $$m\angle1=2n+10,\ m\angle2=4n-32,\ and\ m\angle L=60\degree$$ find $$m\angle G$$

Type answer here

Correct Answer: 16

Deg^°

Rad

A line or segment that passes through the midpoint of a side of a triangle and is also perpendicular to that side. Perpendicular bisectors do not always pass through the opposite vertex.

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​Perpendicular Bisector

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Open Ended

In triangle ABC, DE is a perpendicular bisector of AC with D on AC. If $$AD=2y+4,\ CD=y+12,\ and\ m\angle EDC=5\left(x-12\right).$$ Find x and y. Find AD, DC, and AC