In this lesson students return to conjectures they made in a previous unit that the construction of an angle bisector is valid, and that isosceles triangles have a line of symmetry. Now that students know how to use transformations to prove parts congruent, as well as the triangle congrence theorems, they can prove these conjectures. In the warm-up students look for and make use of structure (MP7) as they make connections between steps in a construction and justifications for why the construction is valid. In both the subsequent activity and the optional activity, students critique the reasoning of others (MP3) as they read and comment on proofs in various states of completeness.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Critique others' reasoning (in spoken and written language) about constructions.
- Justify (in writing) that the angle bisector construction works.
- Justify (orally) that the perpendicular bisector construction works.
- Let’s prove that some constructions we conjectured about really work.
- I can critique a proof about constructions.
- I can explain why constructions work.
A quadrilateral with four right angles.
A quadrilateral with four congruent sides.