Converse to the Pythagorean Theorem

Question 1

Which math sentence can be used to determine if this triangle is a right triangle?

Revolt · Accepted Answer

12 squared + 15 squared = 18 squared

Question 2

In an isosceles triangle, the longest side measures c units. The other sides of the triangle measure a units. Which equation can be used to determine if the triangle is a right triangle?

Revolt · Accepted Answer

2 a squared = c squared

Question 3

Chelsea is making a kite in the shape of a triangle. To determine if the triangle is a right triangle, Chelsea completed the following steps.Step 1:Find the side lengths of the triangle: 30 inches, 24 inches, 18 inches. Step 2: Substitute the values into the Pythagorean theorem: .Step 3:Combine like terms: .Step 4: Evaluate each side: .Chelsea says the triangle is not a right triangle. Which best describes the accuracy of her explanation?

Revolt · Accepted Answer

The triangle is actually a right triangle. In step 3, Chelsea incorrectly rewrote the expression on the left side of the equation.

Question 4

James cut out four parallelograms, the dimensions of which are shown below. Parallelogram 1length: 12 in.width: 15 in.diagonal: 20 in.Parallelogram 2length: 16 in.width: 30 in.diagonal: 34 in.Parallelogram 3length: 20 in.width: 21 in.diagonal: 29 in.Parallelogram 4length: 18 in.width: 20 in.diagonal: 26 in.James put the parallelograms together so one vertex from each paper exists on a point, as shown in the circle.Which statement explains whether or not the parallelgrams can be put together so each occupies one-quarter of the area of the circle without overlapping any other pieces? Check all that apply.

Revolt · Accepted Answer

The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 1 do not form right angles.; The quadrilaterals cannot be placed such that each occupies one-quarter of the circle because the vertices of parallelogram 4 do not form right angles.

Question 5

Which math sentence can be used to determine if this triangle is a right triangle?

Revolt · Accepted Answer

20 squared + 21 squared = 29 squared

Question 6

Which of these four sets of side lengths will form a right triangle?Set 14 cm, 5 cm, 6 cmSet 2 8 in., 12 in., 20 in.Set 310 mm, 20 mm, 30 mmSet 412 ft, 16 ft, 20 ft

Revolt · Accepted Answer

Set 4

Question 7

Which best explains why this triangle is or is not a right triangle?

Revolt · Accepted Answer

This triangle is a right triangle: .

Question 8

Jude is making a door for a door frame with an opening that measures 9 feet by 3 feet. Which diagonal length should he use to make a door that fits in the door frame?

Revolt · Accepted Answer

feet

Question 9

The areas of the squares formed by the side lengths of the triangles are given for each triangle below. Which triangles are right triangles? Select the three correct answers. (Figures are not drawn to scale.)

Revolt · Accepted Answer

4 squares form a triangle. The squares have areas 9 inches squared, 25 inches squared, 16 inches squared.; 5 squares form a triangle. The squares have areas 25 inches squared, 169 inches squared, 144 inches squared.; 7 squares form a triangle. The squares have areas 64 inches squared, 225 inches squared, 289 inches squared.

Question 10

Javier has four cylindrical models. The heights, radii, and diagonals of the vertical cross-sections of the models are shown in the table. Model 1radius: 14 cmheight: 48 cmdiagonal: 50 cmModel 2radius: 6 cmheight: 35 cmdiagonal: 37 cmModel 3radius: 20 cmheight: 40 cmdiagonal: 60 cmModel 4radius: 24 cmheight: 9 cmdiagonal: 30 cmIn which model does the lateral surface meet the base at a right angle?

Revolt · Accepted Answer

Model 2

Converse to the Pythagorean Theorem Answers

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