Translations
What is a translation?
A slide of a figure in a specific direction and distance.
A reflection is like what real-world action?
A mirror image / flip.
What is the center of rotation?
The fixed point around which a figure turns.
What does it mean for two figures to be congruent?
One can be mapped onto the other using rigid transformations.
What is the sum of the interior angles of a triangle?
180°
Point A(2, 3) is translated 4 units right. What are the new coordinates?
A′(6, 3)
Reflect (3, 5) across the x-axis. What are the coordinates?
(3, −5)
A 90° rotation is a turn of how much of a full circle?
One-fourth of a full turn.
If two figures are congruent, what can you say about corresponding side lengths?
They are equal.
Two angles of a triangle are 50° and 60°. Find the third angle.
70°
A translation moves every point 3 units left and 5 units down. What is the coordinate rule?
(x, y) → (x − 3, y − 5)
Reflect (−4, 2) across the y-axis. What are the coordinates?
(4, 2)
Rotate (2, 1) 90° counterclockwise about the origin. What is the image?
(−1, 2)
If ∠A = 65° and ∠A corresponds to ∠D in a congruent figure, what is ∠D?
65°
Two parallel lines are cut by a transversal. Corresponding angles have what relationship?
They are congruent (equal in measure).
A point moves from (−2, 4) to (3, 1). Describe the translation.
5 units right and 3 units down.
What happens to a point’s distance from the line of reflection?
It stays the same; the line of reflection is the perpendicular bisector.
Rotate (−3, 4) 180° about the origin. What is the image?
(3, −4)
A 6-by-4 rectangle is congruent to another rectangle. What is the area of the second rectangle?
24 square units.
If one angle in a triangle is 90° and another is 35°, find the third.
55°
Triangle ABC is translated. AB = 7 cm before the move. What is A′B′?
7 cm — translations preserve length.
A triangle is reflected across a line. Its area changes from 24 square units to what?
24 square units — reflections preserve area.
A 270° counterclockwise rotation is equivalent to what smaller clockwise rotation?
90° clockwise.
Explain why a mirror-image triangle can still be congruent to the original.
A reflection is a rigid transformation, so it can map one triangle onto the other.
Why can rigid transformations help show that triangle angles sum to 180°?
They preserve angle measure and can reposition the triangle’s angles to form a straight angle.