1. 4.5 isosceles and Equilateral Triangles -Theorem 4.3: Isosceles Triangle theorem says if 2 sides of a triangle are congruent, then the angles opposite those sides are congruent -Theorem 4.4: Converse of Isosceles Triangle theorem says if 2 angles of a triangle are congruent, then the sides opposite those angles are congruent -Theorem 4.5: the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base

2. 4.5 isosceles and equilateral triangles -Corollary to Theorem 4.3: If a triangle is equilateral, then it is equiangular -Corollary to Theorem 4.4: If a triangle is equiangular, then it is equilateral

3. 4.6 Congruence in Right Triangles -Theorem 4.6: Hypotenuse Leg Theorem says if the hypotenuse and a leg of 1 right triangle are congruent to the hypotenuse and leg of another triangle, then the 2 triangles are congruent

4. 5.1 Midsegments of Triangles -Midsegment: connects the midpoint of two sides -Theorem 5.1: If a segments joins the midpoints of 2 sides of a triangle, then the segment is parallel to the 3 rd side, and is half its length

5. 5.2 Perpendicular and angle bisectors -Theorem 5.4: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle. -Theorem 5.5: If a point is equidistant from the sides of the angle, then the point is on the angle bisector

6. 5.3 bisectors in triangles -Theorem 5.6: The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices.

7. 5.3 bisectors in triangles -Circumcenter: Point of concurrency of perpendicular bisectors of a triangle (is center of circle circumscribed about triangle)

8. 5.3 bisectors in triangles -Theorem 5.7: The bisectors of the angles of a triangle are concurrent at a point equidistant from the Sides of the triangle. -Incenter: Point of concurrency of the angle bisectors of a triangle (is center of circle inscribed in triangle)

9. 5.4 Medians and altitudes -Theorem 5.8: The medians of a triangle are concurrent at a point 2/3 distant from each vertex to the midpoint of the opposite side.

10. 5.4 Medians and altitudes -Altitude: perpendicular segment from a vertex of a triangle to the line containing opposite side. -Theorem 5.9: The lines that contain the altitudes of a triangle are concurrent.