Download Review 5A: Special Segments and Points of Concurrency

Date
Name
Per,
Review 5A: Special Segments and Points of Concurrency
1. Any point on the perpendicular bisector of AB is
from endpoints A and B.
2. If point X is on i4£), then
1.
3. PQ is the perpendicular bisector of MN. What is QNl
N
I
!
4. Any point on the angle bisector of Z.A is
from the
5. DH and DG are angle bisectors of AEGH. Find mZEHD and the distance from D to GH.
of the angle.
6. Let WT, NR. and EI be the medians for A W E N , then O is the
find the side lengths below.
Given: W O = 4
01 = 31/2
RO = 4!/2
. Use the given values to
ET = 8
W N = 12
RW = 5
W
N
E
T
Find:
0N=
WT-
EN^
Perimeter of A lyE'A^ =
Perimeter of A WC>£'= _
7. Given that point O is the centroid, which must be true?
a. ^CAX = LB AX
b.
LCBY
=
EI =
c
ABAX
c. OY = OZ
d. CO = 2-0Z
3
z
^
8. The midsegments have been drawn for all sides of liNPO. Use the given values to find the angles and
side measures below.
Given: N Q = 5
PAP 2012
QR = 6
m/.QRO = 3 5 °
m/.QOR = 7 5 °
9. SQ is a midsegment of ANOP. What is the length of OP ?
N
Sx + 6
10. PQ is a midsegment of A A B C . WTiich statement is impossible?
a. AP^ = PC
b. PQ II BC
c.
= BC
d. Z^IPQ ^ ^ACB
11. Find the orthocenter of A W Y X with vertices W ( l , 2), X(7, 2), and Y(3, 5).
Graph AYEA on the grid and answer the following questions. Write all linear equations in point-slope
form and then graph them on the grid to verify the accuracy of your answers.
Y (-2, 6) E (4,-6) A (-4,0)
12. Find the equation of the line containing the median to
AE
13. Find the equation of the line containing the
perpendicular bisector to YE.
-r
c
u
r
i
J
2
1
14. Find the equation of the line containing the
midsegment fromF>l to YE .
i
7 -6 - > i - 3 -2 - 1.
1
1
^ 4 ;
'J
fl
-s
1
PAP 2012
15. Verify the equation found for the midsegment #13 is correct by doing the following:
a.
Compare the length of the midsegment to the length of AE . Is the midsegment half as long?
b. Find the slope of each line to show they are parallel.
16. Find the centroid.
17. Find the circumcenter.
18. Find the orthocenter.
19. Explain the how finding the circumcenter and orthocenter of a triangle is the same and different.
20.
Given: OE is an altitude
OH = OM
Statements
Reasons
Prove: OE is a median for AOHM
O
H
E
M
21. Draw an example and nonexample of three lines intersecting at the point of concurrency.
22. *Points of Concurrency Song* For each paragraph draw and label a triangle with the special segments
and the point of concurrency.
23. Compare and Contrast altitude, median, perpendicular bisector, angle bisector, and midsegment.
24. List the steps to writing the equation of altitude, median, and perpendicular bisector.
25. Explain the difference in location of the orthocenter, circumcenter, incenter, and centroid in a triangle.
PAP 2012