# Geometry Unit 7 Lesson 3 Answers

This has two parst. The first part is the practice, the second part is the quiz.

Practice - 8 Questions

1. Which theorem explains why the circumcenter is equidistant from the vertices of a triangle?

Answer - B. Concurrency of perpendicular

2. Which of the statements about the picture below are true? Choose all that apply.

Answers - B. F is the incenter of the triangle, D. F is the point of concurrency of the angle bisectors of the angles of the triangle, and F. F is equidistant from the three sides of the triangle. (Answers - B, D, and F)

3. If the circumcenter of a triangle lies on the triangle, then what type of triangle is it?

Answer - B. right

4. Find the coordinates of the circumcenter of ABC with the vertices A(0,0), B(3,0), and C(3,2).

Answer - B. (1.5, 1)

5. Find the coordinates of the circumcenter of ABC with vertices A(1,4), B(1,2), and C(6,2).

Answer - D. (3.5, 3)

6. Part A - In the figure, P is the incenter of isosceles RST. What type of triangle is RPT?

Answer - A. isosceles

Part B - In the triangle, if m<RST=64, then what is m<RPT?

Answer - D. 122

7. In the figure below, point H is the incenter of DEF, and m<DEF=130. What is the measure of <DEF?

Answer - C. 80

8. Part A - Find the value of x.

Answer - A. x=2

Part B - In the previous question, what is the distance from a side of the triangle to the incenter?

Answer - 7 units

Bisectors in Triangles Quiz Part 1 - 8 questions

1. Find the length of the midsegment. The diagram is not to scale.

Answer - C. 40

2. Use the information in the diagram to determine the height of the tree.

Answer - A. 60

3. Which statement is not necessarily true? Given: DE is the bisector of JL

Answer - A. DK=KE

4. Find the circumcenter of the triangle.

Answer - B. (-5/2, -2)

5. Where is the circumcenter of any given triangle?

Answer - B. the point of concurrency of the perpendicular bisectors of the sides of the triangle

6. Where can the perpendicular bisectors of the sides of a right triangle intersect?

Answer - B. II only

7. What part of the coordinate plane is equidistant from the points A(-3,2) and B(3,2)? Explain your answer.

Answer - all points on a line perpendicular to the line between those two points and through a point halfway between the two points

m = (Y2-Y1)/(X2-X1) slope between

m' = -1/m slope of perpendicular, the line we want

y = m' x + b

to get b (point halfway between)

average x = (-3+3)/2 = 0

average y = (2+2)/2 = 2

so through (0 , 2)

2 = m' * 0 + b

b = 2

y = m' x + 2

8. Lisa, Bree, and Caleb are meeting at an amusement park. They each enter at a different gate. On this diagram of the park, explain how the friends could calculate the point that is equidistant from all three gates.

Answer - First, you should make a triangle out of all of the points. Then you will find the midpoint of it all. Last, make lines from the midpoint to each point that is adjacent. That's where you will see there intersection.

I don't have the answers to the second half of the quiz. It differs for everybody. But besides that, 100% Hope this helps!