--- title: "Polygons" subtitle: "Angles and shapes · Classifying shapes · Lesson 9" --- # Polygons **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Stop signs are octagons, honeycomb cells are hexagons, and a star is a polygon with corners that point in. What makes some of them regular? :::teacher-note **In one sentence:** Students change the number of sides and drag corners to see polygons named (pentagon to decagon), regular or irregular, and convex or concave, and reason about why equal sides alone are not enough (AC9M7SP02, node 3). **Students should be able to say:** I can name polygons from 3 to 10 sides. I can tell whether a polygon is regular, and explain why. I can tell a convex polygon from a concave one. **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 Picture pushing two opposite corners of a regular hexagon towards each other. :::keep-together **A hexagon has six equal sides. Must it be a regular hexagon?** ☐ Only if it is convex ☐ No: its angles might not be equal ☐ Yes: equal sides make it regular My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** No. Squash a regular hexagon and the sides stay equal but the angles change. Regular needs equal sides and equal angles. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Names and properties :::keep-together ### Count, then check Here is the routine for naming a polygon. 1. $\text{6 sides} \Rightarrow \text{hexagon}$ — Count the sides for the name. 2. $\text{sides equal and angles equal?}$ — Both: regular. Either one fails: irregular. 3. $\text{an angle} > 180^\circ?$ — Yes: concave (a corner points in). No: convex. 4. $\text{square} = \text{regular quadrilateral}$ — A rhombus has equal sides but not equal angles; a rectangle the reverse. Now match the names. **Match each polygon to its number of sides.** A. 7 B. 6 C. 10 D. 8 E. 5 {{columns 60% 40%}} {{rows 1}} | Part | Letter | |---|---| | `pentagon` | | | `hexagon` | | | `heptagon` | | | `octagon` | | | `decagon` | | ::: :::teacher-note **Answer:** pentagon → E. 5; hexagon → B. 6; heptagon → A. 7; octagon → D. 8; decagon → C. 10 Pent- five, hex- six, hept- seven, oct- eight (an octopus has eight arms), dec- ten. ::: :::keep-together ### Find the mistake **Kim decides whether a rhombus is regular. Click the line where her reasoning goes wrong.** ``` 1 This rhombus has four sides of 5 cm. 2 Its angles are 60°, 120°, 60° and 120°. 3 All its sides are equal, so it is a regular quadrilateral. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: regular needs equal angles too, and 60° and 120° are not equal. The only regular quadrilateral is a square. ::: :::keep-together ### Concave **How can you tell that a polygon is concave?** ☐ At least one corner points in, with an angle more than 180° ☐ It has a right angle ☐ It has more than six sides ☐ Its sides are not all equal ::: :::teacher-note **Answer:** At least one corner points in, with an angle more than 180° A concave polygon has a corner that points in: a reflex angle, over 180°. ::: :::typical ## One change at a time **A concave pentagon.** Each task changes one thing. **An irregular octagon.** **Rectangles.** **Circles.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Polygons :::keep-together ### Names **What is a polygon with 9 sides called?** ☐ Heptagon ☐ Octagon ☐ Decagon ☐ Nonagon ::: :::teacher-note **Answer:** Nonagon 9 sides: a nonagon. ::: :::keep-together ### Regular **Which is a regular polygon?** ☐ A rhombus with angles 70° and 110° ☐ An equilateral triangle ☐ A rectangle 4 cm by 6 cm ☐ An isosceles triangle ::: :::teacher-note **Answer:** An equilateral triangle An equilateral triangle has equal sides and equal angles (60° each). ::: :::keep-together ### A regular hexagon **Each angle of a regular hexagon is the same. The angles add to 720°. How big is each one, in degrees?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 120 720 ÷ 6 = 120°. ::: :::keep-together ### Review: angle sums **Review: what do the angles of an octagon add to, in degrees?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1080 (8 − 2) × 180 = 1080°. ::: ## Make: a dart Then: is your dart regular? Why can a concave polygon never be regular? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A pentagon has angles 100°, 110°, 110°, 100° and 120°. Is it regular? Convex or concave?** {{lines-3}} ::: :::teacher-note **Answer:** Irregular (its angles are not equal), convex (every angle under 180°). :::