--- title: "Classifying triangles" subtitle: "Angles and shapes · Classifying shapes · Lesson 7" --- # Classifying triangles **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Roof trusses, bridges and set squares are all triangles, but not the same kind. Builders name them by their sides and their angles, because that tells you how they fit together. :::teacher-note **In one sentence:** Students drag triangles on a dot grid and see them named by sides (scalene, isosceles, equilateral) and by angles (acute, right, obtuse), combine the two names, and reason about impossible pairs (AC9M7SP02, node 1). **Students should be able to say:** I can name a triangle by its sides and by its angles. I can explain why some triangles are impossible, like a right-angled equilateral triangle. I can use equal sides and equal angles to find missing angles. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Think of a square cut in half along a diagonal. :::keep-together **Can a triangle be right-angled **and** isosceles?** ☐ No: a right-angled triangle can't have equal sides ☐ Yes ☐ Only if it is equilateral My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** Yes: angles 90°, 45° and 45°, with the two sides at the right angle equal (half a square, cut along its diagonal). ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Two names :::keep-together ### Sides, then angles Here is the routine for naming a triangle. 1. $90^\circ, 45^\circ, 45^\circ$ — A triangle with these angles: two are equal, so the sides opposite them are equal. 2. $\text{isosceles}$ — Sides name: two equal sides. 3. $\text{right-angled}$ — Angles name: the biggest angle is 90°. Give both: isosceles, right-angled. 4. $60^\circ, 60^\circ, 60^\circ$ — Equilateral means equal angles too, so an equilateral triangle is always acute. Now try one: sides 5, 5 and 8. **A triangle has sides 5 cm, 5 cm and 8 cm. Name it by its sides.** ☐ Right-angled ☐ Isosceles ☐ Scalene ☐ Equilateral ::: :::teacher-note **Answer:** Isosceles Two equal sides: isosceles. ::: :::keep-together ### Find the mistake **Zara names a triangle by its angles. Click the line where her reasoning goes wrong.** ``` 1 A triangle has angles 110°, 40° and 30°. 2 It has two acute angles, 40° and 30°. 3 So it is an acute triangle. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: every triangle has at least two acute angles. The biggest angle decides: 110° is more than 90°, so it is obtuse. ::: :::keep-together ### Impossible pairs **Which of these triangles is impossible?** ☐ An obtuse isosceles triangle ☐ An acute scalene triangle ☐ A right-angled scalene triangle ☐ A right-angled equilateral triangle ::: :::teacher-note **Answer:** A right-angled equilateral triangle An equilateral triangle has three equal angles, 60° each: none can be 90°. ::: :::typical ## One change at a time **Make it scalene.** Each task changes one thing. **Obtuse and scalene.** **Nearly equilateral.** **Two right angles?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Naming triangles :::keep-together ### Equal angles **A triangle has angles 50°, 50° and 80°. Name it by its sides and its angles.** ☐ Isosceles and obtuse ☐ Scalene and acute ☐ Isosceles and acute ☐ Equilateral and acute ::: :::teacher-note **Answer:** Isosceles and acute Two equal angles sit opposite two equal sides: isosceles. The biggest angle, 80°, is under 90°: acute. ::: :::keep-together ### A right angle **A triangle has angles 25°, 65° and 90°. Name it.** ☐ Scalene and right-angled ☐ Isosceles and right-angled ☐ Scalene and obtuse ☐ Scalene and acute ::: :::teacher-note **Answer:** Scalene and right-angled No equal angles, so no equal sides: scalene. One 90° angle: right-angled. ::: :::keep-together ### Base angles **An isosceles triangle has one angle of 40° between its two equal sides. What is each of the other two angles, in degrees?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 70 180 − 40 = 140, shared equally: 70° each. ::: :::keep-together ### Review: angle sum **Review: a triangle has angles 35° and 85°. What is the third, in degrees?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 60 180 − 35 − 85 = 60°. ::: ## Make: obtuse and isosceles Then explain why the obtuse angle has to be the one between the equal sides. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A triangle has angles 30°, 30° and 120°. Name it by its sides and its angles.** {{lines-3}} ::: :::teacher-note **Answer:** Isosceles (two equal angles, so two equal sides) and obtuse (120°). :::