Parallel and perpendicular lines PowerPoint includes proof

This PowerPoint starts by reminding students of concepts gradient, perpendicular and parallel. There are couple questions in the middle to check the understanding of perpendicular and parallel before proceeding to the proof, which is the beef of this presentation. The proof is, why will the gradients of two perpendicular lines multiply to -1. The proof is introduced step by step using pictures. To have a full lesson, you would need to add some questions/worksheet to the end. This presentation is fully editable Microsoft PowerPoint.

The right age group is middle school. Common core standard is HSG.GPE.B.5 (Expressing geometric properties with equations) however be aware that this is a bit more formal approach than a purely graphical explanation would be. So, students need to be somewhat ready to understand a bit of abstraction like "this line represents any random line" and so on.

Outline: Finding gradient from a picture (5 pages), finding constant from a picture, collecting the equation, parallel lines (5 pages), perpendicular lines and gradients (example), proof that gradients of two perpendicular lines multiply to -1. (8 pages). In total 24 slides.