Worksheets5-2 Bisectors in Triangles
Total questions: 20
Worksheet time: 48mins
What is the definition of a perpendicular bisector of a triangle?
A line that connects two vertices of the triangle
A line that passes through the midpoint of a side of the triangle and is perpendicular to that side.
A line that divides the triangle into two equal parts
A line that is parallel to one of the sides of the triangle
How many perpendicular bisectors does a triangle have?
4
2
3
5
What is the definition of an angle bisector of a triangle?
A line that divides an angle into two equal angles
A line that divides an angle into three equal angles
A line that divides a triangle into two equal parts
A line that connects the midpoints of two sides of a triangle
In a triangle, if the angle bisectors are concurrent, what is the name of the point of concurrency?
centroid
orthocenter
circumcenter
incenter
In a triangle, if the perpendicular bisectors are concurrent, what is the name of the point of concurrency?
centroid
orthocenter
circumcenter
incenter
How can you use perpendicular bisectors to find the circumcenter of a triangle?
By finding the point of intersection of the perpendicular bisectors of the sides of the triangle.
By finding the midpoint of the sides of the triangle
By finding the point of intersection of the medians of the triangle
By finding the point of intersection of the altitudes of the triangle
Explain how to use angle bisectors to find the incenter of a triangle.
Measure the angles of the triangle and find the average
Connect the midpoints of the sides of the triangle
Draw the perpendicular bisectors of the sides and find their intersection point
Draw the angle bisectors of the triangle and find their intersection point
What conditions would be enough to prove that P is the circumcenter of △HJK? Select all that apply.
L, M, and N are the midpoints of HK , HJ , and KJ
PL≅PM≅PN
PH≅PJ≅PK
△HJK is an acute triangle
What is the radius of the inscribed circle of △HJK?
2
6
10
22
What are the coordinates of the circumcenter of △ABC?
(−1,0.2)
(0,−1)
(−1,−1)
(−1,0)
Points D, E, and F are the midpoints of the sides of △ABC. Which point is the center of a circle that contains A, B, and C?
T
D
P
F
Which point is the center of a circle that intersects each side of △ABC at exactly one point?
T
D
P
F
Points D, E, and F are the midpoints of the sides of △ABC. If TA = 8.2, what is TC?
What is the value of GF?
What is the value of BC? [Round to the nearest tenth]
If XY = 24, XZ = 22, and JQ = 5, find the value of the circumscribed circle of △XYZ. [Round to the nearest tenth if necessary]
If XY = 24, XZ = 22, and JQ = 5, find the value of QK. [Round to the nearest tenth if necessary]
In △ABC, AB has midpoint M, and ℓ is the perpendicular bisector of AB and the angle bisector of ∠ACB. Which of the following must be true? Select all that apply.
The radius of the inscribed circle of △ABC is AM.
AC = CB
Both the circumcenter and incenter of △ABC are on ℓ.
The circumcenter of △ABC is inside the triangle.
Circle O intersects AB only at F, BC only at G, and AC only at H. Which equation is true?
AH = AC
m∠OFB = 90°
OB = OC
OF = OC
∠BAO ≌ ∠ABO
What is the area of the patio not covered by the blue sunshade? [Round to the nearest whole number]
