Transformations and Congruence flashcards

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TranslationTranslations: A slide that moves every point the same distance in the same direction.
Coordinate rule for a translation by (a,b)?Translations: (x,y) → (x+a,y+b).
What moves during a translation?Translations: Every point moves by the same vector.
Does a translation change side lengths?Translations: No.
Translation by (−2,3) moves a point how?Translations: 2 left and 3 up.
What is a zero translation?Translations: (x,y) → (x,y).
Vector from P(x,y) to P′(u,v)?Translations: (u−x,v−y).
Vector from (1,2) to (5,3)?Translations: (4,1).
Do all points share one vector in a translation?Translations: Yes.
What does a negative horizontal component mean?Translations: Move left.
What does a positive vertical component mean?Translations: Move up.
Is translation a rigid motion?Translations: Yes.
Does translation preserve angle measure?Translations: Yes.
Does translation reverse orientation?Translations: No.
Can translation change area?Translations: No.
Are a figure and its translated image congruent?Translations: Yes.
Reflection across x-axis?Reflections: (x,y) → (x,−y).
Reflection across y-axis?Reflections: (x,y) → (−x,y).
What happens to a point on the mirror axis?Reflections: It stays fixed.
Reflection across y=x?Reflections: (x,y) → (y,x).
Reflection across y=−x?Reflections: (x,y) → (−y,−x).
What happens to points on y=x when reflected there?Reflections: They stay fixed.
Does reflection preserve distance?Reflections: Yes.
Does a reflection reverse orientation?Reflections: Yes.
How far are corresponding points from the mirror line?Reflections: Equally far.
What does the mirror line do to the point-image segment?Reflections: Perpendicularly bisects it, unless the point is on the line.
Is a figure congruent to its reflection?Reflections: Yes.
90° CCW about origin?Rotations: (x,y) → (−y,x).
90° CW about origin?Rotations: (x,y) → (y,−x).
Which direction is counterclockwise?Rotations: Opposite a clock hand’s usual direction.
180° about origin?Rotations: (x,y) → (−x,−y).
Are 180° clockwise and counterclockwise rotations the same?Rotations: Yes.
What is a half turn?Rotations: 180°.
Does repeating a 180° rotation restore the original?Rotations: Yes.
What is a center of rotation?Rotations: The fixed point around which a figure turns.
Does rotation preserve lengths?Rotations: Yes.
Does rotation preserve orientation?Rotations: Yes.
Does the center move under rotation?Rotations: No.
Are rotated figures congruent?Rotations: Yes.
Name three rigid motions.Rigid Motions and Symmetry: Translation, reflection, rotation.
What do rigid motions preserve?Rigid Motions and Symmetry: Distance and angle measure.
Is a dilation of scale 2 rigid?Rigid Motions and Symmetry: No.
Does a rigid motion preserve area?Rigid Motions and Symmetry: Yes.
Can a rigid motion change a figure’s size?Rigid Motions and Symmetry: No.
What is a composition of transformations?Rigid Motions and Symmetry: Applying transformations in sequence.
Does transformation order always commute?Rigid Motions and Symmetry: No.
Which step happens first in “reflect, then translate”?Rigid Motions and Symmetry: Reflect.
Can two reflections make a translation or rotation?Rigid Motions and Symmetry: Yes, depending on mirror lines.
How do you track a composition?Rigid Motions and Symmetry: Apply each coordinate rule in the stated order.
Line symmetry means?Rigid Motions and Symmetry: A reflection maps the figure onto itself.
Rotational symmetry means?Rigid Motions and Symmetry: A turn less than 360° maps the figure onto itself.
Does every square have line symmetry?Rigid Motions and Symmetry: Yes.
Smallest positive rotational symmetry angle of a square?Rigid Motions and Symmetry: 90°.
Does every figure have nontrivial symmetry?Rigid Motions and Symmetry: No.
How can rigid motions establish congruence?Triangle Congruence: Map one figure exactly onto the other.
Are corresponding sides of congruent triangles equal?Triangle Congruence: Yes.
Are corresponding angles of congruent triangles equal?Triangle Congruence: Yes.
Does reflection prevent congruence?Triangle Congruence: No.
Can a dilation of factor 2 show congruence?Triangle Congruence: No.
What does SSS mean?Triangle Congruence: Three pairs of corresponding sides congruent.
What does SAS mean?Triangle Congruence: Two sides and the included angle congruent.
What does ASA mean?Triangle Congruence: Two angles and the included side congruent.
What does AAS mean?Triangle Congruence: Two angles and a non-included side congruent.
Does AAA prove triangle congruence?Triangle Congruence: No; it shows similarity.
Does SSA generally prove congruence?Triangle Congruence: No.
What does HL apply to?Triangle Congruence: Right triangles.
What must match for HL?Triangle Congruence: Hypotenuse and one corresponding leg.
Why is SSA called ambiguous?Triangle Congruence: The conditions can fit more than one triangle.
Does HL apply to arbitrary non-right triangles?Triangle Congruence: No.