Tenth graders learn the two special right triangles — the 45-45-90 (with equal legs) and the 30-60-90 — whose fixed side ratios let you find missing sides instantly, without a calculator.
Students will be able to…
Some right triangles have such predictable proportions that you can find any side in your head. What are these special triangles, and what are their magic ratios?
Project each item and have students use the special-triangle ratios. The tool explains the fixed side relationships.
Tap any phase to open the teacher moves and student actions.
Some right triangles have magic proportions — which ones?
Teacher models.
Class uses Special Triangle Ratios.
Students solve.
One triangle.
Aligned to the Common Core State Standards for Mathematics (High School Geometry).
Understand side ratios in right triangles lead to trigonometry.
Use trigonometric ratios and the Pythagorean theorem to solve right triangles.
Prove theorems about triangles.
Know precise definitions of geometric figures.
Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.
Have students use special right triangles to solve real problems — like finding the diagonal of a square or the height of an equilateral triangle. A printable special-triangles sheet is in the Math library.
Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.
A quick self-check with instant feedback, drawn from this lesson’s key terms.
A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.