Prove It (Part 1)

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Objective

Students will be able to develop and prove hyptheses about angles in triangles, in preparation for the next lesson, in which they will develop a proof of the Pythagorean theorem.

Big Idea

Students work on proving hypotheses – and end up proving the Pythagorean Theorem.

Lesson Author

Beth Menzie

Amsterdam, NY

Grade Level

Tenth grade

Subjects

Math

similar triangles

Geometry

Similarity and Congruence

triangle (Determining Measurements)

Standards

HSG-CO.C.9

Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

HSG-CO.C.10

Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

HSG-SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Introductory Problem

10 minutes

ProveItPart1_IntroProblemNarrative.docx page 1

Proving Hypotheses

30 minutes

ProveItPart1_ProvingHypothesesNarrative.docx page 2

Closure

5 minutes

With about five minutes to go, I ask the students to stop working and I let them know that I’d like each group to report out on their progress with the Parallel Lines problem.