Parallelogram ABCD is rotated 90° counterclockwise. What rule shows the input and output of the rotation, and what is the new coordinate of A′?
(x, y) → (−x, −y); A′ is at (5, −1)
(x, y) → (−y, x); A′ is at (−1, −5)
(x, y) → (y, −x); A′ is at (1, 5)
(x, y) → (x, −y); A′ is at (−5, −1)
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
If ≅ , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If ≅ , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If ≅ , then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If ≅ , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.

The proof, with a missing reason, proves that the measure of ∠ECB is 22°.

Statement
Reason
m∠ADE = 68°
Given
m∠DAE = 90°
Definition of a right angle
m∠AED = 22°
Triangle Sum Theorem
joins the midpoints of and
Given
is parallel to
?
∠ECB ≅ ∠AED
Corresponding angles are congruent
m∠ECB = 22°
Substitution property

Which of the following can be used to fill in the missing reason?

Triangle Inequality Theorem
Midsegment of a Triangle Theorem
Concurrency of Medians Theorem
Isosceles Triangle Theorem