L3.11 - Splitting Triangle Sides with Dilation, Part 2
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Prove that a segment parallel to one side of a triangle divides the other sides proportionally (in writing).[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Explain why a segment parallel to one side of a triangle divides the other sides proportionally.[/*][/list]
11.1: Notice and Wonder: Parallel Segments
What do you notice? What do you wonder?
11.2: Prove It: Parallel Segments
Does a line parallel to one side of a triangle always create similar triangles?
1. Create several examples. Decide if the conjecture is true or false. If it’s false, make a more specific true conjecture.
2. Find any additional information you can be sure is true. Label it on the diagram.
3. Write an argument that would convince a skeptic that your conjecture is true.
11.3: Preponderance of Proportional Relationships
[img width=281px;,height=233px;]https://lh5.googleusercontent.com/tBF64oLqC1Y-yPTByXVjMBUAX3vFjvRzCG08sboOG8_hkmeIvlzT4-NrJFa2NBeR3puK2Oq2Ho8CtiYBRjUbpthgECA1TTRlfDAYkJY_0Bemw7tuj01vPRUV0l-JongSlC2qAcWpDyA[/img][br]1. Find the length of each unlabelled side.[br]Segments AB and EF are parallel. [br][img width=195px;,height=25px;]https://lh3.googleusercontent.com/lnXEut2DfJo3PTQBbAh97T4uaCZ0FhTTQMhaBok0_ngbNqyVefnYYfpJfoeA47Ze8SF-l66_R3lOyY8ELL4-cpWGwSad9uFJngEJ47QFWXgKlFyoYPL3MgklmLFXzqgGD9zQp6hnemY[/img]
[img width=287px;,height=212px;]https://lh3.googleusercontent.com/hQk8kGPGE8UPF5-KvWMvTlhilEJEAb7B6TCRQmd2kMbrlx5iAwYdYbG4ryeBT7NYOq_hozUj5HxpLXyC-ILXoC0XV8xyf9a0Iu5zmBV4eNUiM4leZ1JSoW70yw9PF4KrxwOe1qwI2bU[/img][br]2. Find the length of each unlabelled side.[br]Segments BD and FG are parallel. Segment EG is 12 units long. Segment EB is 2.5 units long.[br][img width=88px;,height=25px;]https://lh3.googleusercontent.com/jY60dWCsABm1mh9jjHrBcDbV06-bRn3ee6D0jiFX1BU6f-CXQT_ENuE-DfhjAZpkKhGEFxtb2_SGibIhRYDFXv-mtt2ZMllGXcbrG4ydtaraeLes0iafceATEGJe5Cphb35AV-3pIKI[/img]
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Prove that a segment parallel to one side of a triangle divides the other sides proportionally (in writing).[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Explain why a segment parallel to one side of a triangle divides the other sides proportionally.[/*][/list]
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