Hanna's Pythagoras Scribepost

3.For the triangle shown, Kendra wrote
the Pythagorean relationship as
r2 = p2 + q2. Is she correct? Explain.

Kendra is incorrect. Leg²+leg²=hypotenuse². Since the legs are r and q and the hypotenuse is p, it should be r²+q²=p² or q²+r²=p².

8.Is the triangle shown a right triangle?
Explain your reasoning.

The triangle shown is not a right triangle. For this triangle to be a right triangle, the area of the two smaller squares must equal the area of the larger one. The area of the two smaller squares are 40 cm² and 20 cm² and the area of the larger square is 50 cm². 40+20=60 cm². 60 cm² does not equal 50 cm² because it is 10 cm² greater.

11.The side lengths of a triangle are 5 cm,
6 cm, and 8 cm. Determine whether the
triangle is a right triangle. Explain

This is not a right triangle since the sum of the areas of the two smaller squares aren't equal to the larger square. 6²=36 cm², 5²=25 cm², 8²=64 cm². 36+25=61. 61 doesn't equal 64.

16.Baldeep is building a wooden box for
storing coloured pencils. The box will have
rectangular sides that are 12 cm wide and
20 cm long. Show how Baldeep can be sure
the sides are rectangular, without using
a protractor.

To make sure that the sides are rectangular, I think that Baldeep should make a diagonal line on the rectangle to separate it into two triangles and make squares with the length, width, and the diagonal line you made. Baldeep should then measure the diagonal line and find the areas of the squares and add the areas of the two smaller squares together to see if it is equivalent to the area of the larger square. If it's the same, that means that it is a right triangle which makes the other triangle a right triangle too. If both triangles are right triangles, then the sides are rectangular.