Activity 2.2: Key Discussion & Inquiry Questions
This activity is a bank of questions designed to move students beyond simple identification and toward a deeper, conceptual understanding of triangle properties. Use these questions to spark whole-class discussions, facilitate think-pair-share activities, or as journal prompts. The goal is to encourage students to articulate their observations and justify their reasoning using the applet as evidence.
Questions for Guided Exploration
These questions are organized to follow a natural learning progression, from simple observation to complex synthesis.1. Warm-Up & Observation Questions (Getting Started)
- "As you drag one vertex to make a side longer, what do you notice about the angle directly across from it?"
- "If you make one angle very wide (obtuse), what happens to the other two angles?"
- "What changes when you move one corner? What stays the same?"
- "When you successfully created an isosceles triangle, what did you notice about the two angles opposite the two equal sides?"
- "Is there a rule connecting the longest side with the largest angle? What about the shortest side and the smallest angle? Describe the pattern you see."
- "Explore an equilateral triangle. What is always true about its angles? Does this explain why an equilateral triangle can only ever be acute?"
- "The Impossible Triangle Challenge": Ask students to attempt to build the following and then explain why they are unable to do so.
- "Why can't you create a triangle with two right angles (90° each)?"
- "Why is a triangle with two obtuse angles impossible to build?"
- "Can you build a Right Equilateral triangle? Why or why not?"
- "Challenging Assumptions":
- "If I rotate the triangle so it's upside down, does its classification change? Why not?"
- "Can a 'tall and skinny' triangle have the same classification as a 'short and wide' one? Create an example."
- "Which classification by sides (scalene or isosceles) can be paired with all three angle types (acute, right, and obtuse)?"
- "Based on your experiments, if you know the measures of two angles in a triangle, can you predict the third? What rule do you think all three angles in any triangle follow?" (This is a great lead-in to the Triangle Angle Sum Theorem, that all angles add up to 180°.)