MEDIAN - a special segment that connects a vertex of a triangle to the midpoint of the opposite side. Every triangle has three medians.

ALTITUDE - a segment that is perpendicular to a side of a triangle, and it intersects with the vertex opposite that side. Most altitudes rise from the base and their length is also the height of the triangle, but any side can have an altitude.

ANGLE BISECTOR - a special segment of a triangle that bisects an angle of the triangle and then intersects the opposite side of the triangle.

PERPENDICULAR BISECTORS - a line or segment that passes through the midpoint of a side of a triangle and is also perpendicular to that side. Perpendicular bisectors do not always pass through the opposite vertex.

Theorems and Postulates

• a point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment
• a point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment
• a point on the bisector of an angle is equidistant from the sides of the angle
• a point in the interior of an angle and is equidistant from both sides of the angle, then the point lies on that angle's bisector
• LL - if the legs of a right triangle are congruent to the corresponding legs of another right triangle, then the triangles are congruent
• HA - if the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the two triangles are congruent
• LA - if one leg and one acute angle of a right triangle are congruent to the corresponding leg and acute angle of another triangle, then the two triangles are congruent
• HL - if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent

Pencils ready...

Draw an example of the following -

1) Triangle RST with median SN

2) Triangle ABC with altitude BD

3) Triangle XYZ with angle bisector WZ

For numbers 4 - 6 determine if triangle ABC is congruent to triangle XYZ and justify your answers

4) AB = XY and angle B = angle Y

5) YZ = BC and XZ = AC

6) AB = XY and YZ = BC

7) Given: angles Q and S are right angles and angle 1 = angle 2

Prove: triangle PQR is congruent to triangle RSP

8) Given: AC _|_ BE , CE_|_ AB , angle BAE = angle DEA

Prove: BE = AD

9) Given: BA = AD and AC = DF

Prove: angle C = angle F