Geometry- Centroid and Orthocenter assignment

G is the centroid of triangle ABC. What is the length of GF? ___ units

26

G is the centroid of triangle ABC. What is the length of AE? ___ units

39

Which figure has an orthocenter outside the triangle?

C

S is the centroid of triangle XYZ. What is the length of SW? 5 units 11 units 22 units 28 units

b. 11

Manny says that the diagram shows a centroid. Is he correct? Why or why not? no, because the centroid is where the altitudes meet no, because the centroid is where the medians meet yes, because the centroid is where the altitudes meet yes, because the centroid is where the medians meet

b. no, because the centroid is where the medians meet

S is the centroid of triangle NQL. What is the length of NR? 4 units 8 units 36 units 48 units

c. 36 units

What error did Tracy make? She used AG = 2EG, but the correct statement is 2AG = GE. She found that x = 4, but the correct value for x is 2. She used GF = 2BG, but the correct statement is BG = 2GF. She found that GF = 64, but the correct value of GF is 8.

c. She used GF = 2BG, but the correct statement is BG = 2GF.

To prove that the medians of an isosceles triangle meet at a point, show that the ________ of a side lies on the line containing the opposite _________ and the point where the other two _________ intersect.

midpoint median vertex