Geometry: Review 5.3 – 5.4
Name_______________________________________________
Use the information in the diagram to find the measure.
1. Find AD.
2. Find mEFH.
3. Find mJKL.
Can you conclude that BD bisects ABC? Explain.
4.
5.
6.
8.
9.
11.
12.
Find the value of x.
7.
Can you find the value of x? Explain.
10.
Find the indicated measure.
13. Point G is the incenter of ACE.
Find BG.
14. Point P is the incenter of HKM.
Find JP.
Find the value of x that makes N the incenter of the triangle.
15.
16.
G is the centroid of ∆ ABC, AD = 8, AG = 10, and CD = 18. Find the length of the segment.
17. BD
18. AB
19. EG
20. AE
21. CG
22. DG
Is BD a perpendicular bisector of ∆ ABC? Is
23.
BD a median? an altitude?
24.
25.
Find the measurements.
26. Given that AB = BC, find AD and mABC.
27. Given that G is the centroid of ABC, find FG and BD.
Copy and complete the statement for HJK with medians
28. PN = ____ HN
29. PL = ____ JP
HN , JL , and KM , and centroid P.
30. KP = ____ KM
Point G is the centroid of ∆ ABC. Use the given information to find the value of x.
31. CG = 3x + 7 and CE = 6x
32. FG = x + 8 and AF = 9x – 6
33. BG = 5x – l and DG = 4x – 5
Complete the sentence with always, sometimes, or never.
34. The median of a triangle is __________________ the perpendicular bisector.
35. The altitude of a triangle is _________________ the perpendicular bisector.
36. The medians of a triangle __________________ intersect inside the triangle.
37. The altitudes of a triangle __________________ intersect inside the triangle.
Point of
Concurrency
What meets there?
Where is it located?
Cicumcenter
Acute: Obtuse: Right:
Incenter
Acute: Obtuse: Right:
Centroid
Acute: Obtuse: Right:
Orthocenter
Acute: Obtuse: Right:
Relationships/ Properties