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
compared to the length of
Explain your answer.
as
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.