8th Grade Math Flashcards: Understand Congruence Through Transformations

What this deck covers

This deck focuses on Understand Congruence Through Transformations, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What does it mean for two plane figures to be congruent using rigid motions?

Answer: One can be obtained from the other by translations, rotations, and reflections. Rigid motions preserve size and shape while moving figures.

Flashcard 2: What is the image of $P(3,-4)$ after reflection across the $y$-axis?

Answer: $P'(-3,-4)$. Reflect across $y$-axis: negate $x$-coordinate.

Flashcard 3: What is the image of $P(-2,5)$ after the translation $(x,y)\rightarrow(x+4,y-3)$?

Answer: $P'(2,2)$. $(-2+4, 5-3) = (2,2)$.

Flashcard 4: Identify the transformation: $(x,y)\rightarrow(x,-y)$.

Answer: Reflection across the $x$-axis. Negating $y$ flips points across the $x$-axis.

Flashcard 5: Identify the transformation: $(x,y)\rightarrow(-x,y)$.

Answer: Reflection across the $y$-axis. Negating $x$ flips points across the $y$-axis.

Flashcard 6: Identify the transformation: $(x,y)\rightarrow(y,-x)$.

Answer: Rotation $90^\circ$ clockwise about the origin. $(x,y) o (y,-x)$ rotates $90°$ clockwise.

Flashcard 7: Identify the transformation: $(x,y)\rightarrow(-x,-y)$.

Answer: Rotation $180^\circ$ about the origin. Negating both coordinates rotates $180°$.

Flashcard 8: Identify the transformation: $(x,y)\rightarrow(x+3,y-2)$.

Answer: Translation right $3$ and down $2$. Add $3$ to $x$, subtract $2$ from $y$.

Flashcard 9: What is a rotation of a figure in the plane?

Answer: A turn about a fixed center by a specified angle and direction. Points rotate around a center point.

Flashcard 10: What is the image of $P(1,6)$ after a $90^\circ$ counterclockwise rotation about the origin?

Answer: $P'(-6,1)$. $90°$ counterclockwise: $(1,6) o (-6,1)$.

Flashcard 11: What is a translation of a figure in the plane?

Answer: A slide that moves every point the same distance in the same direction. Every point moves by the same vector.

Flashcard 12: Which sequence maps a figure to its mirror image across the $y$-axis without changing size?

Answer: Reflect the figure across the $y$-axis. Reflection preserves size while creating mirror image.

Flashcard 13: What is the minimum information needed to describe a rotation precisely?

Answer: Center of rotation, angle measure, and direction. Must specify where, how much, and which way to rotate.

Flashcard 14: Which transformations are rigid motions that preserve distance and angle measure?

Answer: Translations, rotations, and reflections. These transformations preserve distances and angles.

Flashcard 15: Identify the transformation: $(x,y)\rightarrow(-y,x)$.

Answer: Rotation $90^\circ$ counterclockwise about the origin. $(x,y) o (-y,x)$ rotates $90°$ counterclockwise.

Flashcard 16: What is the coordinate rule for translating a point by $\langle a,b\rangle$?

Answer: $(x,y)\rightarrow(x+a,y+b)$. Add $a$ to $x$-coordinate and $b$ to $y$-coordinate.

Flashcard 17: What does a rotation do to a figure relative to a fixed point?

Answer: Turns the figure around a center by a given angle and direction. All points maintain their distance from the center.

Flashcard 18: What does a reflection do to a figure relative to a line?

Answer: Flips the figure across a line, creating a mirror image. Each point maps to its perpendicular distance on opposite side.

Flashcard 19: What is the coordinate rule for reflecting a point across the $x$-axis?

Answer: $(x,y)\rightarrow(x,-y)$. Negate the $y$-coordinate while keeping $x$ unchanged.

Flashcard 20: Which transformations are rigid motions that always preserve congruence?

Answer: Translations, rotations, and reflections. These three transformations preserve distances and angles.

Flashcard 21: What property of distance is preserved by any rigid motion?

Answer: All segment lengths (distances) stay the same. Rigid motions preserve the shape and size of figures.

Flashcard 22: What property of angle measure is preserved by any rigid motion?

Answer: All angle measures stay the same. Rigid motions don't change the shape of figures.

Flashcard 23: What does a translation do to every point of a figure on the coordinate plane?

Answer: Moves every point the same distance in the same direction. Translation slides without rotating or flipping.

Flashcard 24: What is the coordinate rule for a $270^\circ$ counterclockwise rotation about the origin?

Answer: $(x,y)\rightarrow(y,-x)$. Swap coordinates and negate the new $y$-coordinate.

Flashcard 25: What is the coordinate rule for reflecting a point across the line $y=x$?

Answer: $(x,y)\rightarrow(y,x)$. Swap coordinates to reflect across the diagonal.

Flashcard 26: What is the coordinate rule for reflecting a point across the $y$-axis?

Answer: $(x,y)\rightarrow(-x,y)$. Negate the $x$-coordinate while keeping $y$ unchanged.

Flashcard 27: Which sequence maps $(x,y)$ to $(-x,y)$: reflect across $x$-axis or across $y$-axis?

Answer: Reflect across the $y$-axis. Changing $(x,y)$ to $(-x,y)$ negates only $x$-coordinate.

Flashcard 28: Find the image of $S(-6,4)$ after a $180^\circ$ rotation about the origin.

Answer: $S'(6,-4)$. Apply rule $(x,y)\rightarrow(-x,-y)$ to get $(-(-6),-4)=(6,-4)$.

Flashcard 29: Find the image of $R(3,-2)$ after a $90^\circ$ counterclockwise rotation about the origin.

Answer: $R'(2,3)$. Apply rule $(x,y)\rightarrow(-y,x)$ to get $(-(-2),3)=(2,3)$.

Flashcard 30: Find the image of $Q(-4,1)$ after reflection across the $y$-axis.

Answer: $Q'(4,1)$. Reflecting across $y$-axis changes sign of $x$-coordinate.