Prove the Isosceles Triangle Theorem
Topic Index | Geometry Index | Regents Exam Prep Center


Present the following discovery activity as a group activity, class demonstration, enrichment project, extra credit, etc.

Task:  Prove the theorem that states:  "If two sides of a triangle are congruent, the angles opposite those sides are congruent."

Steps:

 1.  Using your compass and straight edge, construct an isosceles triangle.

2.  Using your compass and straight edge, bisect the vertex angle.

3.  Using your drawing, prove that the base angles are congruent.  This may be done in paragraph form or in a two-column format.  Remember that you cannot use the theorem you are trying to prove as a reason in your proof.

 

Note to teachers:  Hopefully, the introductory construction component will suggest a method of proof for students.

Proof:
Statements Reasons
1.  1.  Given
2.  2. Each angle has one unique angle bisector.
3. 3. An angle bisector is a ray whose endpoint is the vertex of the angle and which divides the angle into two congruent angles.
4. 4. Reflexive Property.  A quantity is congruent to itself.
5. 5. SAS - If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
6. 6. CPCTC - Corresponding parts of congruent triangles are congruent.