Points of Concurrency

Triangle Segments and Points of Concurrency

Math I Name______Unit 6, Part II Review Date______

MM1G3. Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

Use the following triangle segment and point of concurrency terms to fill in the blanks: incenter, orthocenter, circumcenter, centroid, midsegment, perpendicular bisector, angle bisector, median and altitude.

Fill in the blank.

1. The medians of a triangle meet at the ______.

2. The segment that separates an angle in a triangle into two congruent parts is the ______.

3. The altitudes of a triangle meet at the ______.

3. The ______is where the perpendicular bisectors of the sides meet.

4. The ______is a segment from the vertex of a triangle to the midpoint of the opposite side of a triangle.

5. The angle bisectors of a triangle meet at the ______.

6. A segment that connects midpoints of two sides of a triangle is a ______.

7. Match the following terms with the correct figure:

angle bisectors, perpendicular bisectors, medians, altitudes

_____ 8. In the diagram below, D, E, and F are all midpoints. What is the value of EB?

A) 8 C) 18

B) 4 D) 16

Use the diagram to the right to answer questions 9-11.

_____ 9. If ZT is 10, what is TV?

A) 20 B) 15 C) 5 D) 4

_____ 10. If YU is 18, what is TU?

A) 9 B) 6 C) 12 D) 8

_____ 11. If XV is 7, what is YV?

A) 7 B) 14 C) 3.5 D) 21

_____ 12. True or False: A median will always go through a vertex.

A) True B) False

_____ 13. True or False: An altitude will always go through a midpoint.

A) True B) False

_____ 14. In the diagram to the right, the perpendicular bisectors

are shown dashed. If BD is 14, what is AD?

A) 7 B) 28 C) 14 D) 5

_____ 15. A perpendicular bisector is a median.

A) sometimes B) always C) never D) I don’t know

_____ 16. In the diagram below, AE is an altitude. If angle ABE is 30°, what is angle BAE?

A) 90°

B) 45°

C) 70°

D) 60°

_____ 17. In the diagram below BD is an angle bisector. If angle CBD is 4x - 2 and

angle ABD is 7x - 35, then what is the value of angle ABC?

A) 34

B) 84

C) 11

D) 42

18. Which two points are always inside the triangle?

a) orthocenter & centroid

b) centroid & incenter

c) incenter & orthocenter

d) circumcenter & centroid

19. The incenter is also the center of the circle inscribed inside the triangle.

a) true

b) false – the incenter is outside

c) false – the orthocenter is the center of the inscribed circle

d) false – the incenter is the center of the circumscribed circle

20. In the diagram to the right, if segment AC = 6x - 12 and

segment EF = 2x + 2, solve for x and the length of each

segment.

x = ______

AC = ______

EF = ______