Which transformation slides every point of a figure the same distance in the same direction? — Translation.A translation moves every point by the same vector (a, b), sliding the figure without turning or flipping it.
A rigid motion preserves which two properties? — Distance and angle measure.Rigid motions (isometries) preserve both distance (side lengths) and angle measure, keeping the figure congruent to the original.
Which of the following is NOT a rigid motion? — Dilation.Dilation changes the size of a figure (scales it), so it does not preserve distances and is not a rigid motion.
What is the image of point P(−3, 5) after a translation by vector (4, −2)? — (1, 3).Add the vector components: (−3 + 4, 5 + (−2)) = (1, 3).
Reflecting point (2, −4) across the x-axis gives which image? — (2, 4).Reflection across the x-axis maps (x, y) → (x, −y). So (2, −4) → (2, 4).
Reflecting point (5, 3) across the line y = x gives which image? — (3, 5).Reflection across y = x swaps coordinates: (x, y) → (y, x). So (5, 3) → (3, 5).
A rotation of 180° about the origin maps (x, y) to which point? — (−x, −y).A 180° rotation about the origin maps every point (x, y) to (−x, −y).
Two figures are congruent if and only if one can be mapped onto the other by what type of transformation? — A composition of rigid motions.Congruence is defined by the existence of a finite composition of rigid motions (translations, rotations, reflections) mapping one figure onto the other.
SSS congruence requires how many pairs of equal sides? — 3.SSS (Side-Side-Side) requires all three pairs of corresponding sides to be equal.
Which congruence criterion applies when two sides and the angle BETWEEN them are equal? — SAS.SAS (Side-Angle-Side) requires two pairs of equal sides and the included angle (the angle between those sides) to be equal.
Does SSA (Side-Side-Angle) always guarantee triangle congruence? — No — it is the ambiguous case.SSA does not guarantee congruence — it is the ambiguous case where two different triangles may fit the given measurements.
HL (Hypotenuse-Leg) congruence applies only to which type of triangles? — Right triangles.HL requires one pair of equal hypotenuses and one pair of equal legs. It applies exclusively to right triangles.
If △ABC ≅ △DEF, which angle corresponds to ∠B? — ∠E.In the congruence statement △ABC ≅ △DEF, vertices correspond in order: A↔D, B↔E, C↔F. So ∠B corresponds to ∠E.
Which criterion uses two angles and a NON-included side? — AAS.AAS (Angle-Angle-Side) uses two pairs of equal angles and one pair of equal sides, where the side is not between the two angles.
Given △ABC and △DEF with AB = DE, BC = EF, and AC = DF, which criterion proves congruence? — SSS.All three pairs of corresponding sides are equal, so SSS (Side-Side-Side) proves congruence.
CPCTC stands for what? — Corresponding Parts of Congruent Triangles are Congruent.CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent" — used after triangles are proven congruent to conclude individual parts are equal.
In a two-column proof, what appears in the left column? — Statements.A two-column proof has Statements in the left column and Reasons (justifications) in the right column.
What is the first statement in almost every two-column proof? — The given information.Proofs begin by stating the given information, which is justified by the reason "Given."
What does the Reflexive Property state? — a = a (any quantity equals itself).The Reflexive Property states every quantity is equal to itself: a = a. It is used to establish a shared side or angle in congruence proofs.
What does the Symmetric Property state? — If a = b then b = a.The Symmetric Property states if a = b then b = a — equality can be written in either order.
What does the Transitive Property state? — If a = b and b = c then a = c.The Transitive Property states if a = b and b = c, then a = c — equality is "passed through" a middle value.
CPCTC can only be used in a proof AFTER what has been established? — The triangles are congruent.CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is a conclusion that follows from proven triangle congruence — it cannot be a reason before congruence is established.
Which reason justifies: "M is the midpoint of AB, therefore AM = MB"? — Definition of midpoint.The Definition of midpoint states that a midpoint divides a segment into two equal parts.
A proof ends with "△ABC ≅ △DEF" justified by "SAS." What type of statement is this? — The final conclusion.The final line of a proof states what was to be proved (the "Prove" statement). Here, △ABC ≅ △DEF is the conclusion of the proof.
When two parallel lines are cut by a transversal, corresponding angles are: — Congruent.Corresponding angles (same position at each intersection) are congruent when the lines are parallel.
Co-interior (same-side interior) angles formed by a transversal cutting parallel lines are: — Supplementary.Co-interior (same-side interior) angles are supplementary — they sum to 180° — when the lines are parallel.
The sum of the interior angles of any triangle is: — 180°.The Triangle Angle-Sum Theorem states that the three interior angles of any triangle always add to 180°.
In a parallelogram, opposite angles are: — Congruent.In a parallelogram, opposite angles are congruent (equal). Consecutive angles are supplementary.
The diagonals of a parallelogram: — Bisect each other.In a parallelogram, the diagonals bisect each other — they cut each other at their midpoints.
If two parallel lines are cut by a transversal and a co-interior angle is 110°, what is the other co-interior angle? — 70°.Co-interior angles sum to 180°. So the other angle is 180° − 110° = 70°.
An exterior angle of a triangle equals: — The sum of the two non-adjacent interior angles.The Exterior Angle Theorem states an exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles.
In a parallelogram, opposite sides are: — Parallel and equal.By definition, a parallelogram has two pairs of opposite sides that are both parallel and equal in length.