In the coordinate plane below, Figure WXYZ is similar to Figure
Part A
Figure is obtained by applying 2 successive transformations to Figure WXYZ. Describe the transformations that could have been applied. State the coordinates that result after each transformation.
Part B
Explain how each transformation affects the coordinates.
Part C
Is the length of rational or irrational? Explain your answer.
Part D
What effect does the dilation have on the length of as compared to the length of Explain your answer.
Triangle FGH has side lengths of 5 cm, 13 cm, and x cm. What would the values of x need to be in order for the triangle to be considered a right triangle?
The figure shows a right triangle and three squares.
Explain how the squares can be used to demonstrate the Pythagorean Theorem.
The diagram shows that and are all parallel. The length of is 10 inches and the length of is 2 inches.
Part A
What is the length of Show your work.
Part B
What is the length of Show your work.
Part C
What is the length of Show your work.
Aisha used the three square tiles shown to model the converse of the Pythagorean Theorem. She used a side length from each of the square tiles to form a right triangle.
Part A
Draw a diagram showing how to arrange the square tiles to create a right triangle. Label each square tile with the appropriate area.
Part B
Using the areas in Part A, write the equation that shows how the sum of the squares of two legs’ lengths equals the square of the hypotenuse length. Explain the equation you wrote.
Part C
Describe a method for approximating the length of the hypotenuse to the tenths place. Explain your work.
Thomas drew a right triangle on a coordinate plane. The base of the triangle has two vertices located at (-3, -5) and (2, -5). If the hypotenuse has a length of 13 units, what is the value for the y-coordinate of the third vertex of the triangle located in quadrant 1?
Line segments PS and QT intersect at point R. Point R is a vertex of right triangle RPQ.
Part A
What is the measure of angle PQR? Show your work and explain your answer.
Part B
What is the length of segment RQ? Show your work.