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5.3a Circumcenters Worksheet
Name _________________________________
Per ______ Seat # ______ Date ___________
5.3 Practice K
Review: Fill in the missing blanks for the following 3 questions.
The circumcenter is the point of concurrency of the _____________________________ of a triangle.
Where is the circumcenter for an acute triange? ____________________________________________
Where is the circumcenter for an obtuse triangle? ___________________________________________
Find the coordinates of the circumcenter of each triangle.
1.
Find the indicated measure.
2.
5.1 Form K Midsegments of Triangles
Write an equation to show that the length of the
midsegment is half the length of its parallel segment.
Then find the value of x.
21.
22.
X is the midpoint of MN . Y is the midpoint of ON .
23. Find XZ.
24. If XY = 10, find MO.
25. If m∠M is 64, find m∠XYZ.
Use the diagram at the right for Exercises 26 and 27.
26. What is the distance across the lake?
27. Is it a shorter distance from A to B or from B to C? Explain.
The midpoints of the sides of ∆ABC
are F, E, and D. If the perimeter of ∆FDE
is 18, then the perimeter of
∆ABC
is _______.
5.2 Practice K
Answer parts a and b below for questions 1-9.
a. Name what theorem that best describes the problem.
b. Set up an equation and solve for x.
Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment,
then it is equidistant from the endpoints of the segment.
Perpendicular Bisector Converse: If a point is equidistant from the endpoints of a segment,
then it is on the perpendicular bisector of the segment.
Angle Bisector Theorem: If a point is on the bisector of an angle, then it is equidistant from the sides of the angle.
Angle Bisector Converse: If a point in the interior of an angle is equidistant from the sides of an angle,
then it is on the angle bisector.
1.
2,
a.
b.
4.
3.
a.
b.
a.
b.
5.
a.
b.
7.
6.
a.
b.
a.
b.
8.
a.
b.
9.
a.
b.
a.
b.
Writing: Determine whether A must be on the bisector of ∠LMN. Explain.
29.
30.