Justifying Mathematical Ideas & Arguments — Visual Lab
Module 2 is where a drawing stops being enough. A geometric claim earns belief only when every step is justified — by a definition, a postulate, or a theorem. This lab lets you move the geometry yourself and watch the relationships that proofs are built on hold true, no matter how you drag.
Module 02 · 44 days · TEKS G.4 · G.5 · G.6
Angle & Proof Explorer
Two live tools. Drag the handles, switch the highlighted pair, and watch the measures justify themselves.
What You're Seeing · Try This
A short tour, then four moves to make the theorems reveal themselves.
What you're seeing
In Parallel Lines & Transversal, two parallel lines (note the matching arrowheads) are crossed by one slanted line. Eight angles form. Pick a pair-family on the right and the lab shades the matching wedges and states why they're equal — or, for co-interior angles, why they add to \(180^{\circ}\).
In Triangle Angle Sum, the three interior angles update as you drag any vertex, and they always total \(180^{\circ}\). Reveal the exterior angle at \(C\) to see it equal the sum of the two remote interior angles.
Try this
- Drag the transversal handle. The four angle measures keep changing — but corresponding angles stay equal to each other. What never changes is the relationship.
- Switch to Co-interior (same-side). Read the two measures: they always sum to \(180^{\circ}\). That single fact justifies a whole step in a parallel-lines proof.
- In the triangle tool, drag a vertex until one angle is obtuse. The three still total \(180^{\circ}\) — the angle-sum theorem doesn't care what the triangle looks like.
- Turn on Exterior angle at C and drag \(A\) or \(B\). Confirm the exterior angle equals \(\angle A + \angle B\) every time.
Key Vocabulary & Standards
The words you'll cite in a proof, and the TEKS this lab supports.
- Transversal — a line that crosses two or more other lines.
- Corresponding angles — same position at each intersection; equal when lines are parallel.
- Alternate interior angles — between the parallels, on opposite sides of the transversal; equal.
- Alternate exterior angles — outside the parallels, on opposite sides; equal.
- Co-interior (same-side interior) — between the parallels, same side; supplementary (sum \(180^{\circ}\)).
- Vertical angles — opposite angles at one intersection; always equal.
- Triangle Angle-Sum Theorem — the interior angles of any triangle total \(180^{\circ}\).
- Exterior Angle Theorem — an exterior angle equals the sum of the two remote interior angles.
G.4 logical reasoning & proof · G.5 constructions and angle/segment relationships · G.6 relationships in triangles and parallel lines.
Where to Go Next
Back to the full course, or into the planning documents.
Instructor: Dr. Goodluck Ijezie-Desbois, PharmD · Beta Academy
Reach out by appointment, at
gijezie-desbois@betaacademy.org,
or through ParentSquare.