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Skate and Climbing Gym: Lines That Keep Their Slope worksheet preview

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Skate and Climbing Gym: Lines That Keep Their Slope

Use gym route diagrams and membership models to explain constant slope with similar triangles and derive linear equations.

Grade 8MathInteractive · Printable

Aligned to8.EE.B.6

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 14 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 8
Subject
Math
Question types
Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

  • Students use similar right triangles to explain why slope is constant along a nonvertical line.
  • Students derive equations of the forms y = mx and y = mx + b from slope triangle ratios.
  • Students apply slope and intercept reasoning to gym routes and membership costs.

How to use

Assign after introducing triangle similarity and slope. Have students mark corresponding legs on the route diagrams and show algebra on separate paper.

Curriculum

Common Core standard covered

8.EE.B.6

Use similar triangles to explain why slope is the same anywhere on a line, and derive y = mx and y = mx + b.

Preview

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Skate and Climbing Gym: Lines That Keep Their Slope

Connect similar slope triangles to route and membership equations.

Route Design

The gym uses coordinate drawings to plan straight route sections. Compare horizontal and vertical legs, not diagonal lengths.

The plotted points are the vertices of two right triangles along the same straight route line QOP. Triangle QRO lies to the left of the origin, and triangle OHP lies to the right. The triangle sides are not drawn; sketch them to help you compare the triangles. Each grid unit represents 1 foot.−5−4−3−2−1123450−5−4−3−2−112345OHPQR
1.
Which angle correspondence establishes that triangles QRO and OHP are similar by angle-angle similarity?
  • A. The angle at Q matches the angle at P, and both triangles have a right angle.
  • B. The angle at O in triangle QRO matches the angle at O in triangle OHP, and both triangles have a right angle.
  • C. The angle at Q matches the angle at O in triangle OHP, and both triangles have a right angle.
  • D. The angle at Q matches the angle at H, and both triangles have a right angle.
2.
The gym extends the same straight route beyond P. A new right slope triangle has a vertical rise of 5 feet. Its legs are parallel to the legs of triangle OHP, so the triangles are similar.

What is the new triangle's horizontal run?   feet

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