Right Triangles

Overview

In this first day of the unit “Exploring the Pythagorean Theorem,” students learn what makes a right triangle and why perpendicular sides matter. They build the vocabulary and classification skills needed to identify right triangles and prepare for similarity and trigonometry connections later in the unit.

Learning intentions

Students will be able to:

• Define a right triangle and identify its right angle.
• Explain perpendicular sides using everyday and diagram-based language.
• Classify triangles as right or not right using evidence from diagrams.
• Use correct labels (legs, hypotenuse) when given a right triangle picture.

Success criteria

Students can:

• Point to the right angle and name it as an angle of 90 degrees.
• Describe perpendicular sides as forming a right angle.
• Correctly classify at least 4 out of 5 triangles on the worksheet as right or not right.
• In a right triangle, identify the hypotenuse as the side opposite the 90-degree angle.

Curriculum links

• Geometry - Similarity, Right Triangles, and Trigonometry: Understand right-triangle angle properties and how they connect to trigonometric ratios (as developed later in the unit).
• Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems (previewing the triangle types needed for later lessons).
• Prove the Pythagorean Theorem using triangle similarity (relates to the structural understanding of right triangles built today).
• Derive area formulas from auxiliary perpendicular lines (reinforces the idea that perpendicular lines create predictable geometric relationships).

Lesson structure (30 minutes)

1. 0–4 min · Hook (image/claim). Teacher displays the introduction slides and shows two triangle diagrams—one with a visible 90-degree corner and one without—asking, “Which one is definitely a right triangle, and how do you know?” Students do a quick think-pair-share and write one reason in their notebook.

2. 4–10 min · Direct instruction (definitions). Teacher uses the introduction slides to define “right triangle” (a triangle with one right angle) and “perpendicular sides” (two lines/segments meeting at 90 degrees). Students follow along and underline the phrases “right angle” and “perpendicular” on a class anchor sheet area (or in notes).

3. 10–16 min · Guided practice (identify right triangles). Teacher returns to the introduction slides and shows 4–5 triangle sketches labeled with angle marks or squares at corners. Students use sentence frames to respond: “This is a right triangle because ___,” and “This is not a right triangle because ___.”

4. 16–23 min · Independent check (worksheet). Teacher distributes the introduction right triangle worksheet and gives 2 minutes to work through questions independently, then 2 minutes to revise with a partner if needed. Students classify triangles as right or not right, circle the right angle when present, and identify the hypotenuse in at least two right triangles.

5. 23–28 min · Share-out and misconceptions. Teacher uses the introduction slides to show 2 student work samples (or re-displays the same items) and asks: “What evidence did you use?” and “Where did mistakes happen—right angle identification, or perpendicular sides?” Students justify their answers using the language from the lesson (right angle, perpendicular, opposite 90°).

6. 28–30 min · Exit ticket (1 quick decision). Teacher collects the introduction right triangle worksheet and gives a final question on the board: “Draw a right triangle with perpendicular legs—label the right angle.” Students sketch quickly and label the right angle before turning in.

Resources

• the introduction slides
• the introduction right triangle worksheet
• Student notebooks or scrap paper for hook and exit sketch
• Pencils and erasers
• Visual aids: a small right-angle card (optional) for quick referencing
• Timer for transitions (hook, practice, worksheet, exit)

Assessment

• Formative: listen during think-pair-share for correct use of “right angle” and “90 degrees.”
• Formative: monitor guided practice responses for evidence-based classification.
• Worksheet check: collect the introduction right triangle worksheet to confirm classification and hypotenuse identification.
• Exit ticket: verify students can sketch perpendicular legs and label the 90-degree angle.

Differentiation

• Support: provide the sentence frames (“This is a right triangle because…”, “Perpendicular means…”) and a word bank on the board during guided practice.
• Support: allow students to use a 90-degree angle marker (paper right-angle corner) to test triangles during the worksheet.
• Extension: for students who finish early, ask them to explain in writing why the hypotenuse is the side opposite the 90-degree angle using diagram language.
• EAL/SEN: keep prompts visual and short; accept verbal explanations recorded by the student in simple sentences; allow partner clarification during the worksheet revision phase.