Page 193 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

Instructional Tips
Teachers can:
• support students in posing and solving problems that are relevant to them;
• use geometric representations to reinforce students’ understanding of the side-length
relationship for right triangles; that is, the area of the square extending from the hypotenuse of a
triangle is equal to the sum of the areas of the squares extending from the other two sides;
• support students in identifying the precision to which measurements are needed based on the
context of the problem.
Teacher Prompts
• Identify a real-life situation that might require knowing the relationship between the lengths of the sides of a right triangle.
• Are all triangles that have side lengths in the ratio of 3 to 4 to 5 right triangles?
• What is the relationship between the side lengths of any right triangle?
• If the three side lengths of a right triangle are 5 units, 12 units, and 13 units, name the side
lengths of a triangle similar to it.
• The net of a square-based pyramid is a composite shape. What are the basic shapes in the net?
What dimensions are needed to find the slant height of one of the sides of such a pyramid?
Sample Tasks
1. Have students take a photo of a right triangle in a real-life context. Have them determine the length of its hypotenuse using the side-length relationship. Have them verify their result by measuring the hypotenuse using a measuring tool. If the real-life right triangle can be measured, have students compare its measures with those of the photo to determine its scale factor.
2. Have students use technology to verify the relationship of the sides of a right triangle using shapes other than a square, such as in the examples shown below.
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