--- title: "Angles at parallel lines" subtitle: "Angles and shapes · Parallel lines · Lesson 1" --- # Angles at parallel lines **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Railway tracks, the lines on a car park, the rungs of a ladder: parallel lines crossed by another line. The angles they make come in pairs. :::teacher-note **In one sentence:** Students turn a transversal across two parallel lines, see that the same place at each crossing gives the same angle, and learn to name corresponding, alternate and co-interior pairs in any orientation, keeping them apart from vertically opposite angles (AC9M7M04, node 1). **Students should be able to say:** I can find corresponding, alternate and co-interior angles where a line crosses two parallel lines. I can tell these pairs apart from vertically opposite angles. I can explain that the names say where the angles are, and parallel lines make the pairs equal or add to 180°. **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 the two crossings. Is one a copy of the other? :::keep-together **$a$ is above the top line, on the left of the crossing line. $e$ is in the same place at the bottom crossing. If you turn the crossing line, what happens to $a$ and $e$?** ☐ One grows while the other shrinks ☐ Nothing links them: they change separately ☐ They stay the same size as each other My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** They stay the same size as each other. The parallel lines cross the transversal the same way, so the bottom crossing is a copy of the top one, slid along. a and e are corresponding angles. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## The three pairs :::keep-together ### Find the mistake **Mia names a pair of angles. Click the line where her reasoning goes wrong.** ``` 1 Mia looks at angles b and c. 2 b and c are on opposite sides of the crossing line. 3 So b and c are alternate angles. 4 Alternate angles are equal, so b = c. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: b and c are at the same crossing, opposite each other, so they are vertically opposite. Alternate angles are one at each crossing, between the parallel lines. (Vertically opposite angles are equal too, so line 4's b = c is true, for a different reason.) ::: :::keep-together ### Co-interior **Which pair is co-interior?** ☐ $c$ and $e$ ☐ $c$ and $g$ ☐ $c$ and $f$ ☐ $b$ and $c$ ::: :::teacher-note **Answer:** $c$ and $e$ c and e are both between the lines and both on the left of the crossing line: co-interior. ::: :::typical ## One change at a time **Corresponding.** Each task changes one thing. This board does not name the pairs, so the check tells you. **Co-interior.** **Vertically opposite.** **Not parallel.** **A right angle.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Name the pair :::keep-together ### Name it **$d$ and $e$ are** ☐ corresponding ☐ alternate ☐ vertically opposite ☐ co-interior ::: :::teacher-note **Answer:** alternate Between the lines, on opposite sides: alternate. ::: :::keep-together ### Name it again **$b$ and $f$ are** ☐ corresponding ☐ co-interior ☐ alternate ☐ vertically opposite ::: :::teacher-note **Answer:** corresponding Both above their line, on the right: the same place at each crossing, so corresponding. ::: :::keep-together ### One crossing **$a$ and $d$ are** ☐ corresponding ☐ co-interior ☐ vertically opposite ☐ alternate ::: :::teacher-note **Answer:** vertically opposite At one crossing, opposite each other: vertically opposite. ::: :::keep-together ### Review: a straight line **Review: $a$ and $b$ are on a straight line. $a = 115^\circ$. What is $b$?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 65 Angles on a straight line add to 180°: 180 − 115 = 65°. ::: ## Make: a pair that adds to 180° Find a pair, then turn the crossing line. Do they still add to $180^\circ$? Stretch: which pairs add to $180^\circ$ but are not between the lines? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A transversal crosses two parallel lines. Which angle pairs are equal, and which pair adds to 180°?** {{lines-3}} ::: :::teacher-note **Answer:** Corresponding angles and alternate angles are equal (so are vertically opposite angles); co-interior angles add to 180°. :::