Honors Geometry III Lesson

Proof Playbook: Strategies, Pitfalls, and Power Moves for Geometric Proofs

Shared by A STEM Educator

9thBTC Style / Thinking Classrooms50 min

Learning Objective

Students will identify the structure of a geometric proof, apply key theorems and definitions as justifications, and construct logically valid two-column proofs while diagnosing and correcting common reasoning errors.

Lesson Overview

Students progress from identifying the anatomy of a proof and recognizing valid reasoning, through writing single-step and multi-step justifications, to constructing and critiquing full two-column proofs — building metacognitive habits at every stage.

Materials

Vertical whiteboards or large paper on desks
Dry-erase markers (or pencil and paper)
Pencils

Scaffolded Task Progression

1Task 1

Anatomy Labeling — No writing yet, just reading.

Here is a completed two-column proof. Your job: label each part.

[ Interactive graph / diagram, available in the full lesson ]

Statement	Reason
$△ A B C$ with $m ∠ A = 70°$ , $m ∠ B = 60°$	Given
$m ∠ A + m ∠ B + m ∠ C = 180°$	Triangle Angle Sum Theorem
$70° + 60° + m ∠ C = 180°$	Substitution
$m ∠ C = 50°$	Subtraction Property of Equality

On your board, answer:
(a) What is the Given?(b) What is the Prove (what did we find)?(c) Which step is the 'engine' — the theorem that makes everything possible?(d) Could you swap the order of rows 2 and 3? Why or why not?

2Task 2

Reason Bank — Match the step to its justification.

Below are four proof statements with missing reasons. On your board, write the correct reason next to each statement. Choose from the Reason Bank.

Reason Bank: Definition of Midpoint | Reflexive Property | Segment Addition Postulate | Given

[ Interactive graph / diagram, available in the full lesson ]

Statement	Reason
$M$ is the midpoint of $\overline{A B}$	_____
$A M + M B = A B$	_____
$\overline{A M} ≅ \overline{M B}$	_____
$\overline{A B} ≅ \overline{A B}$	_____

Unlock the full lesson

See all 7 scaffolded tasks, the full answer key, warm-up, exit slip, and a print-ready version — free to start.

Create a free account

Already have an account? Sign in

Make it your own

Like this lesson but want to tweak it?

Make an editable copy and adjust the tasks, warm-up, and answer key to fit your class — no need to start from scratch.

Generate a new lesson