2.1b: Triangle Properties

1. -Special Segments in Triangles 2.1b: Triangle Properties GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios(sine, cosine, tangent) within mathematics or across disciplines or contexts

2. Median • Connects a vertex to the of the opposite side ________ B Tells us that it cut the side BC in half so _____________ F D When you combine ALL the medians of one triangle, you get the _______________ A C E A centroid would balance the triangle if you held it up with a pencil

3. Lets find the centroid of this triangle.

4. Example Determine the coordinates of J so that SJ is a median of the triangle. J = J = J =

5. Altitude Connects the vertex to where it is __________________ to the opposite side Combine all three ALTIUDE’S in a triangle and you get a _______________ A Z T W R P Tells us the segment is perpendicular

6. Example BD is an altitude of Triangle ABC Find BC, and AC 3x-5

7. Angle Bisector • A segment that cuts one vertex angle in __________ and goes to the opposite side of the triangle Draw angle bisector AF B Indicates the angle A was bisected F A C

8. If BG was an angle bisector, what would be the

9. Example N Find m NWB if WT is an angle bisector Of WNB T m NWT = 3x + 8 m NWB = 3x + 34 3x+8 W B

10. Perpendicular Bisector • A segment that: 1) is ________________________ to one side of the triangle 2) ____________ the same side H B O

11. Draw in segment NL if NL is a perpendicular bisector of WB.

12. example • Name all segments that are (if any) • Angle Bisectors • Perpendicular Bisectors • Altitudes • Medians

13. End of notes