Congruent Triangles


A variety of ways of proving triangles congruent are introduced, and plenty of practice in completing two-column proofs is included. Flow-chart proofs are a new format for proving theorems, and coordinate geometry is introduced and related to proofs. The Triangle Midsegment Theorem is stated, proved, and used.

What you can expect to learn

After completing these activities you should be able to

  1. Classify triangles by angle measure and side length.
  2. Prove angle relationships related to triangles.
  3. Identify congruent figures and their corresponding parts.
  4. Prove triangles congruent using SAS, ASA, AAS, and SSS congruence postulates and theorems.
  5. Show that the corresponding parts of congruent triangles are congruent.
  6. Prove theorems related to isosceles and regular triangles.
  7. Recognize that AAA and SSA are not sufficient conditions to prove triangles congruent.
  8. Prove and apply special congruence theorems for right triangles.
  9. Use coordinate geometry to identify characteristics of triangles.
  10. Prove and apply the Triangle Midsegment Theorem.
  11. Describe several ways that architects can use their occupation to glorify God.
Activity List