8.G Tutor Intake -- Transformations, Pythagorean Theorem, and Volume

A line segment is 7 units long. The segment is rotated 90 degrees
about a point and then reflected across a line, so it now sits in a
different place and faces a different direction. What is the length of
the image segment after these rigid motions?

An angle measures 53 degrees. The angle is rotated 40 degrees about a
point. Rotation is a rigid motion. What is the measure, in degrees, of
the image angle? Enter a number.

Under a reflection across the y-axis, a point $(x, y)$ maps to which
image point?

The point $(3, -5)$ is rotated 180 degrees about the origin. The
coordinate rule for a 180-degree rotation about the origin is
$(x, y) \to (-x, -y)$. What is the x-coordinate of the image point?
Enter a number.

In grade 8, two figures are defined to be congruent exactly when:

How does the grade-8 definition of similarity differ from the
definition of congruence?

Triangle ABC is similar to triangle DEF, with vertices corresponding
in that order ($A \leftrightarrow D$, $B \leftrightarrow E$,
$C \leftrightarrow F$). Side $AB = 6$ corresponds to side $DE = 9$.
Side $BC = 8$ corresponds to side $EF$. Using the scale factor, find
the length of side $EF$. Enter a number.

In triangle ABC, angle $A = 50\degree$ and angle $B = 60\degree$. In
triangle PQR, angle $P = 50\degree$ and angle $Q = 60\degree$. By the
Angle-Angle (AA) criterion the triangles are similar. What is the
measure, in degrees, of angle $C$? Enter a number.

A transversal crosses two lines. A pair of alternate interior angles
formed by the transversal measure $70\degree$ and $110\degree$ (they
are not equal). What can you conclude about the two lines?