Isosceles and Equilateral Triangles
I.SectionObjectives
- Prove and use the Base Angles Theorem.
- Prove that an equilateral triangle must also be equiangular.
- Use the converse of the Base Angles Theorem.
- Prove that an equiangular triangle must also be equilateral.
II.ProblemSolvingActivity-TriangleProofs
- Provide students with the definition for the Base Angles Theorem.
- Base Angles Theorem- If two sides of a triangle are congruent, then their opposite sides are congruent, and
the angles opposite the congruent sides are congruent. - Next, assign students the task of proving that this is correct.
- The students need to draw a diagram involving isosceles triangles to demonstrate this theorem.
- Then, they need to write a two- column proof or a flow proof.
- When finished, the students are going to present their work in small groups.
- Allow time for the other students in the group to provide feedback.
- Extension- repeat the exercise with the students working with the converse of the Base Angles Theorem.
- Possibility- you can also assign half the class the Base Angles Theorem and the other half the converse of the
Base Angles Theorem.
III.MeetingObjectives
- Students will draw a design using isosceles triangles.
- The design is to prove the Base Angles Theorem.
- Students will demonstrate understanding through a design and through a verbal explanation.
IV.NotesonAssessment
- Did the students complete the design?
- Does it use isosceles triangles?
- Did the students show the bisection of the triangle?
- Does the diagram show the angles and sides that are congruent?
- Does the proof have the correct statements and reasons?
- Is the student able to explain his/her thinking in words?
- Provide comments/feedback when necessary.
Congruence Transformations
I.SectionObjectives
- Identify and verify congruence transformations.
- Identify coordinate notation for translations.
- Identify coordinate notation for reflections over the axes.
- Identify coordinate notation for rotations about the origin.
Chapter 5. Geometry TE - Problem Solving