Learning Target 4 Name_______________________________________ 5.1 Midsegments Period ___________________

Notes

Midsegment of a triangle:

Example:

MN connects the midpoints of AB and AC MP connects the midpoints of AB and BC NP connects the midpoints of AC and BC

Theorem 5.1 – Midsegment Theorem:

The segment connecting midpoints of two sides of a triangle is ________________ to the third side and is ________________ as long as that side.

For the following problems, !" is a midsegment of ∆!"#. Find the value of x. a. b. c.

For the following problems, use ∆!"#, where A, B, and C are midpoints of the sides.

a. If !" = 3! + 8 and !" = 2! + 24, what is AB?

b. If !" = 3! − 5 and !" = 4! + 2, what is HB? c. If !" = 7! − 1 and !" = 4! − 3, what is GH?

LearningTarget4 Name____________________________________________________5.4AltitudesandMedians Period______________

NotesTheMEDIANofatriangleisasegmentconnectingthe tothe oftheoppositeside.Thepointofconcurrencyforthe3mediansiscalledthe_______________________________.Themediansofatriangleintersectatapointthatis thedistancetotheoppositemidpoint.Example:

AnALTITUDEisa___________________________________________connectingavertextothe_________________________sideofthetriangle.Thepointofconcurrencyforthe3altitudesiscalledthe_______________________________.Summary–fillintheblankandshowapictureofeach: The3Perpendicularbisectorsmeetatthe . The3anglebisectorsmeetat .

The3mediansmeetat . The3altitudesmeetat .