Question

math vocabulary
alternate exterior angles
alternate interior angles
center of dilation
corresponding angles
academic vocabulary
dilation
linear pair
similar
adjacent
enlarge
intersect
reduce
use the unit vocabulary to complete the problems.
lines g and h are parallel lines cut by a transversal. ( mangle7 = 135^circ ).
write the measure of angles 1 - 8 in the figure.
a. what is ( mangle6 )? explain how you know.
( 45^circ )
b. what is ( mangle4 )? explain how you know.
( 135^circ )
c. what is ( mangle3 )? explain how you know.
( 45^circ )
d. what is ( mangle1 )? explain how you know.
( 135^circ )
use what you know about transformations to describe the
relationship between figure pqrs and figure ( pqrs ).
use at least three math or academic vocabulary terms from
this unit in your answer. underline each term you use.

Explanation:

To describe the relationship between figure \(PQRS\) and \(P'Q'R'S'\), we can use the following terms:

• \(\underline{\text{dilation}}\): A transformation that changes the size of a figure.
• \(\underline{\text{similar}}\): Figures that have the same shape but not necessarily the same size.
• \(\underline{\text{center of dilation}}\): The fixed point around which a figure is dilated.

We can observe that \(P'Q'R'S'\) is a smaller version of \(PQRS\). This indicates a dilation. Since the shape is preserved, the figures are similar. The center of dilation can be inferred as the origin (assuming the coordinate system's origin is relevant, though not explicitly marked in the problem statement).

Answer:

\(\underline{\text{Dilation}}\) is used as \(P'Q'R'S'\) is a scaled - down version of \(PQRS\). The figures are \(\underline{\text{similar}}\) because their shapes are the same. The \(\underline{\text{center of dilation}}\) (assumed to be the origin based on coordinate - like structure) is the fixed point for the dilation transformation.