Applying Geometric Concepts in Modelling

Squares are constructed on the legs of a right triangle, as pictured. The area of the small square is 40 square units and the area of the large square is 80 square units. If another square is constructed on the remaining side of the triangle (hypotenuse), what will its area be?

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Sarah is designing a skatepark for her community. She wants to add a ramp for skaters to practice tricks. The ramp needs to be positioned in a way that it aligns with certain specifications for safety and functionality. Sarah's design includes the following features: Line A: represents the edge of the pathway in the skatepark, which is represented on the graph above. Line B: Sarah wants the ramp to be parallel to Line A, ensuring skaters can smoothly transition onto it. Line C: Sarah also plans to install a rail for skaters to grind on. She wants the rail to be perpendicular to Line A, providing an additional challenge for advanced skaters. If both Line B and Line C pass through the point shown in the graph, which equations could describe either of these lines? Choose all that are correct.

Mathematical Equivalence

ON

The grid shows different locations in Henry's town. Each unit represents 1 mile.

What is the distance, in miles, between the Post Office and the Store? Round your answer to the nearest tenth, if necessary.

Mathematical Equivalence

ON

Harrison works at a factory that makes paper cups for water coolers. He calculated the volume of the paper cup as 8 cubic inches. What is the height of the cup? Round your answer to the nearest tenth.

Mathematical Equivalence

ON

Look at the triangle.

Which statements are true? Choose all that apply.

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Mathematical Equivalence

ON

Which statement best describes the relationship between Julie Street and Janet Street?

• Julie Street and Janet Street are both parallel and perpendicular to one another.

• Julie Street and Janet Street are neither parallel or perpendicular to one another.

• Julie Street and Janet Street are parallel to one another.

• Julie Street and Janet Street are perpendicular to one another.