x 34 — — = =

7 2x — = — =

x = = — —

3x 4x+20 — — = =

X A B Y C Z — — —— == = = YZ XY

X B A Y C Z — — == = = —— 7

X B A Y C Z — — == = = ——

parallel congruent transversal congruent transversal

What is a segment from the vertex of the triangle to the midpoint of the opposite side? Median

What is the definition of an Altitude? The perpendicular segment from a vertex of the triangle to the segment that contains the opposite side.

A line that contains the ___________ of one side of a triangle and is _________ to another side passes through the _________ of the third side. midpoint parallel midpoint

What is a line that is perpendicular to a segment at its midpoint and does NOT have to start at a vertex? Perpendicular Bisector

The segment that joins the midpoint of two sides of a triangle…. 1) 2) Is parallel to the third side Is half as long as the third side

Definition of a Centroid Altitude fact about right triangles Altitude fact about obtuse triangles The point where all three medians meet Two of the altitudes of are the legs of the triangle Two of the altitudes are outside of the triangle

If M is the midpoint of XY and MN is parallel to YZ, then line MN is the altitude. If M is the midpoint of XY and MN is parallel to YZ, then N is the midpoint of XZ Error Section!!

— — Both blue lines are a good representation of altitudes. Both blue lines are a good representation of medians NOT altitudes. ==

— — Both lines are a good representation of Perpendicular Bisectors. The orange line are a good representation of Perpendicular Bisectors. The green line is not able to be determined.

These three lines are a good representation of Medians. The teal line is a good representation of a Median. The blue and red lines are good representations of Altitudes.

The intersection of AF, BE, and CD is the centroid. No it is not the centroid. Centroids are formed from medians. Altitudes are displayed here.

MN is the perpendicular bisector of XY, XZ, and YZ. If M is the midpoint of XY and N is the midpoint of XZ, then MN || YZ and MN = 1/2 YZ.

AB C What is the red line an example of? Explain your answer. A Median

What is the red line an example of? Explain your answer. An Altitude A B CD

M L N What is the black line an example of? Explain your answer. A Perpendicular Bisector

Why are these true? If MN = 6, then YZ = 12. If YZ = 20, then MN = 10. Just needs an explanation

What is the red line an example of? Explain your answer. Altitude, Median, and Perpendicular Bisector

What is the yellow line an example of? Explain your answer. None, explain

A B C What are each of these lines? Explain. Red is Altitude, orange is Median, and grey is Perp. Bisector

R 3 K J S 4 What is the length of JK? You will be asked to justify your answer. JK = 6

Construct a Right Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector. Be ready to justify your answer.

Construct an Acute Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector. Be ready to justify your answer.

Construct an Obtuse Triangle and draw in one Altitude, one Median, and one Perpendicular Bisector.

12 — = — = J K Find JK. Be ready to justify your answer.

10x — = — = J K Find x. Be ready to justify your answer. 15x +15

Construct a Centroid. Be ready to justify your answer.