Constructing Triangles
Learn how to construct triangles using ASA, SAS, and SSS methods with a compass, ruler, and protractor. Let's get started! 🚀
Video Lesson
Watch and learn the basics
Flashcards
Review key concepts visually
%20Triangle%20Components.webp)
%20Construct%20Triangle%20(ASA).webp)
%20Construct%20Triangle%20(SAS).webp)
%20Constructing%20Triangles(Common%20Pitfall).webp)
%20Construct%20Triangle%20(SSS).webp)
🛎️ Parts of a Triangle Explained
- The vertices A, B and C are labelled in an anticlockwise direction.
- Each side a, b and c is opposite its matching angle.
🛎️ Constructing a Triangle with Two Angles and the Included Side (ASA)
- The given side is the side between the two known angles.
- Draw the side first, then measure each angle at the ends so they meet at C.
🛎️ Constructing a Triangle with Two Sides and the Included Angle (SAS)
- Draw one side, then use a protractor to draw the angle at one end.
- Measure the second side along the angle to find point C.
🛎️ Common Pitfall: Two Possible Triangles
- With two sides and a non-included angle, there may be two triangles.
- This is called the ambiguous case and both triangles can be correct.
🛎️ Constructing a Triangle with Three Sides (SSS)
- Draw the longest side first to make construction easier.
- Use a compass to draw arcs from each end that meet at point C.
Practice Questions
Test your understanding
You are given two sides ( and ) and the angle between them (). Can a unique triangle be constructed?
Correct! 🎉 +10 pointsNot quite right
When given two sides and the angle between them (Side-Angle-Side), a unique triangle can always be constructed.
You are given two sides ( and ) and the angle between them (). Can a unique triangle be constructed?
Correct! 🎉 +10 pointsNot quite right
When you know two sides and the angle between them (Side-Angle-Side), a unique triangle can always be constructed.
You are given three angles: , , and . Can a triangle be constructed?
Correct! 🎉 +20 pointsNot quite right
A triangle cannot be constructed because the sum of the angles exceeds . A valid triangle must have the sum of its interior angles exactly equal to .
You are given two angles ( and ) and the side between them (). Can you construct a unique triangle?
Correct! 🎉 +20 pointsNot quite right
When given two angles and the side between them (Angle-Side-Angle), a unique triangle can always be constructed.
You are given two angles ( and ) and the side between them (). Can a unique triangle be constructed?
Correct! 🎉 +20 pointsNot quite right
With two angles and the side between them (Angle-Side-Angle), a unique triangle can always be constructed.
You are given three angles: , , and . Can a triangle be constructed?
Correct! 🎉 +30 pointsNot quite right
While the angles add up to , the side lengths are not specified, meaning there are infinitely many triangles with those angle measures but different side lengths.
Want to see the full working?
Interactive Activity
Practice identifying and constructing triangles
Loading interactive widget...
Click here to open ChatCat