Relationships in Triangles


 The first half of this chapter focuses on the intersection points of a triangle’s altitudes, angle bisectors, perpendicular bisectors, and medians. The second half of the chapter covers inequalities in triangles as well as indirect proofs, a valuable tool often used in everyday reasoning and arguments.

What you can expect to learn

After completing these activities you should be able to

  1. Verify and apply the properties of points on the perpendicular bisector of a segment and on an angle bisector.
  2. Identify a triangle’s circumcenter, orthocenter, incenter, and centroid and make related applications.
  3. Construct a triangle’s circumcenter and incenter.
  4. Apply properties of inequality to the sides and angles related to a triangle.
  5. Apply the Greater Angle Theorem and Longer Side Theorem within a triangle.
  6. Complete indirect proofs of algebraic and geometric statements.
  7. Use the Triangle Inequality Theorem to determine whether three segments of given length form a triangle.
  8. Use the Hinge Theorem and its converse to compare the measures of sides and angles in two triangles.
  9. List several ways geometry and carpentry can be used to minister to the physical needs of others and to further the gospel.
Activity List