Triangle 4B

Overview

In this Phlow, students learn to construct a triangle given two sides and the included angle (SAS). Using a ruler, protractor, and compass, they create a triangle with sides of 7 cm and 5 cm and an included angle of 60°. The process builds confidence in tool use, precision, and the logical sequencing of geometric constructions.

Worked Example

1. Draw a 7 cm base line using the ruler.
2. Place the protractor on one end and mark a 60° angle.
3. Draw a ray through the 60° mark to form the angle line.
4. Set the compass to 5 cm and draw an arc from the end of the base.
5. Mark the intersection of the arc and angle line as the apex.
6. Connect the apex to the base endpoints to complete the triangle.

Step Sequence

Draw and label the base accurately using the ruler.
Use the protractor to measure and draw the included 60° angle.
Set compass width to 5 cm and draw an intersecting arc.
Mark the intersection as the apex of the triangle.
Join points to complete the triangle and verify all sides and angles.

Sample Prompts

“Which line represents the base of the triangle?”
“Where should the 60° mark be placed?”
“Which intersection correctly locates the apex?”

Why This Matters

This construction demonstrates that two sides and an included angle define a unique triangle. It links geometry to real-world applications in engineering, architecture, and design while reinforcing mathematical logic, measurement accuracy, and the use of geometric instruments.

Step 1 / 13

Prerequisite Knowledge Required

Triangle 4A – Constructing a triangle given three sides (SSS).
Angles 3B – Measuring and drawing angles with a protractor.
Length 3A – Measuring and marking using centimetres and millimetres.
Drawing Tools 3B – Using compass and ruler correctly.

Main Category

Geometry → Constructions

Estimated Completion Time

Approx. 10–14 seconds per question.
40 questions total → Total time: 7–10 minutes.

Cognitive Load / Step Size

Moderate-to-high. This Phlow integrates multiple instruments — ruler, protractor, and compass — but adds each tool gradually. Each screen introduces one micro-action (draw, measure, set, intersect), ensuring clarity and preventing overload.

Language & Literacy Demand

Low-to-moderate. Short, instructional text supported by visuals. Key mathematical terms (base, apex, 60°, compass) are highlighted in purple, allowing students to focus on geometry rather than heavy reading.

Clarity & Design

High-contrast visuals for ruler, protractor, and compass actions.
Sequential dot navigation reinforces logical step order.
Purple highlights focus on geometric reasoning, not decoration.
A/B layouts show clear contrasts between correct and incorrect constructions.

Curriculum Alignment (ROI Junior Cycle – Geometry & Trigonometry)

Construct triangles given two sides and the included angle (SAS).
Accurately measure and draw angles using a protractor.
Combine instruments to perform precise geometric constructions.

Engagement & Motivation

The use of multiple tools adds a hands-on challenge that feels authentic and practical. Students gain satisfaction from creating a perfect triangle and seeing geometry in action — a bridge between visual reasoning and real-world skill.

Error Opportunities & Misconceptions

Measuring the angle from the wrong side of the base.
Using the wrong protractor scale (inner vs outer).
Setting the compass to the wrong side length.
Missing the correct intersection point for the apex.
Connecting incorrect endpoints when completing the triangle.

Transferability / Real-World Anchoring

High. This technique is foundational for engineering, design, construction, and trigonometry. Understanding the SAS relationship builds intuition for sine and cosine rules in later learning.

Conceptual vs Procedural Balance

Balanced. Students gain procedural fluency through repetition while developing conceptual understanding — recognising that all points on the arc form possible triangles satisfying the given SAS condition.

Learning Objectives Addressed

Construct a triangle given two sides and an included angle (SAS).
Measure and draw angles precisely using a protractor.
Use compass and ruler to locate intersection points accurately.
Understand that two sides and an included angle define a unique triangle.

What Your Score Says About You

Less than 20: You understand the idea but mix up tool order or placement — revisit 4A and Angles 3B.
21–29: You follow steps correctly but may mis-measure or mislabel — double-check angle sides.
31–39: Confident and accurate with solid understanding of SAS construction.
40 / 40: Excellent precision and logic — ready for bisector and altitude constructions (Triangle 4C).