Module 8 TEST REVIEW (8.1-8.4)
NAME: _________________________ Period: ____
Circumcenter theorem
Centroid Theorem
Incenter theorem
Altitude
Orthocenter
Median
Midsegment
Triangle Midsegment Theorem
For 1-8: Fill in the blank with the proper definition from the above word bank. Note each word is used only one time.
1. The __________________ of a triangle is a line segment that connects the midpoint of two sides of the triangle.
2. PA= PB = PC in this figure
defines the ____________________________________ which
states that point P is equidistant (the same distance) to all three vertex points (A, B, C).
3.
A ________________________ connects a vertex to the midpoint of the opposite side of that vertex.
4. PX= PY= PZ in this figure
defines the _______________________ which states that point
P is equidistant (the same distance) to all three sides of the triangle.
5. The ___________________ of a triangle, also referred to as the height of the triangle, is a perpendicular
segment from a vertex to the line containing the opposite side.
6. The intersection of the lines that contain the altitudes of a triangle is the ______________________________.
7. The segment joining the midpoints of the two sides of a triangle is parallel to the third side, and its length is half
the length of that side is known as the _______________________________________________.
8. The below figure describes the ______________________________________ where three medians meet at
point P.
Point P
For 9-12 answer the following related to below figure, given that ZX is a perpendicular bisector of WY
9. What is the m ∠ 𝑌𝑋𝑍?
Answer: __________________
10. If WY is 24cm, what is WX?
Answer: ___________________
11. If WX is 14cm, what is WY?
Answer: ___________________
12. If WZ is 32cm, what is YZ?
Answer: ___________________
For 13 and 14 answer the following related to the below figure given that XE, XF, XD are perpendicular bisectors and
point X is equidistant from the vertices A, B, C.
13. If segment XD is 7cm and XB is 20cm
a. What is the length of segment XA?
Answer: ______________________
b. What is the length of segment XC?
Answer: ______________________
14. If segment BC is 32cm
a. What is the length of segment FC?
Answer: ______________________
b. What is the length of segment BF?
Answer: ______________________
15. Graph the triangle with the given vertices, then find the circumcenter.
K (1, 1), L (1, 7), M (4, 1)
Circumcenter:
For 16-19 use the below figure and given that QX and RX are angle bisectors of PQR
16. What is the distance from X to QR?
17. What is the distance form X to PQ?
18. What is the m ∠ 𝑃𝑄𝑅?
19. What is the m ∠ PQX?
20. What is m ∠ 𝑅𝑄𝑋?
21. Draw the medians from each vertex (A, B, and C) and then locate and identify the centroid.
Centroid (
,
)
Use the figure on the right to answer 22-25 given that point P is the centroid.
22. What is the length of FP?
23. What is the length of FX?
24. What is the length of FH?
25. What is the length of GX?
26. Plot the triangle with points/vertices A (6,2), B(6, -1), C (4,0), then find the orthocenter.
For 27-29 use the figure on the right
27. What is the length of segment JL?
28. What is the length of segment NK?
29. What is the m ∠ 𝑀𝐿𝐾?
30. The vertices of FGH are F(-1, 1), G(-5, 4), and H(-5, -2). X is the midpoint of FG and Y is the midpoint of FH.
Show that XY is parallel to GH and XY = ½ GH