Understand Angle Transformation Properties - 8th Grade Math
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What is the angle-measure rule for a reflection of an angle?
What is the angle-measure rule for a reflection of an angle?
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A reflection maps an angle to a congruent angle (same measure). Reflections flip figures while keeping angles unchanged.
A reflection maps an angle to a congruent angle (same measure). Reflections flip figures while keeping angles unchanged.
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What is the name of a transformation that always preserves angle measure?
What is the name of a transformation that always preserves angle measure?
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A rigid motion (isometry): translation, rotation, or reflection. These transformations preserve distances and angles.
A rigid motion (isometry): translation, rotation, or reflection. These transformations preserve distances and angles.
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What is the angle-measure rule for a translation of an angle?
What is the angle-measure rule for a translation of an angle?
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A translation maps an angle to a congruent angle (same measure). Translations slide figures without changing angles.
A translation maps an angle to a congruent angle (same measure). Translations slide figures without changing angles.
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What is the angle-measure rule for a rotation of an angle?
What is the angle-measure rule for a rotation of an angle?
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A rotation maps an angle to a congruent angle (same measure). Rotations turn figures but preserve angle measures.
A rotation maps an angle to a congruent angle (same measure). Rotations turn figures but preserve angle measures.
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Which word means “same angle measure” for an angle and its image under a rigid motion?
Which word means “same angle measure” for an angle and its image under a rigid motion?
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Congruent. Congruent angles have equal measures.
Congruent. Congruent angles have equal measures.
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What notation states that $ABC$ and $DEF$ have equal angle measure?
What notation states that $ABC$ and $DEF$ have equal angle measure?
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$\angle ABC \cong \angle DEF$. The $\cong$ symbol denotes congruence between angles.
$\angle ABC \cong \angle DEF$. The $\cong$ symbol denotes congruence between angles.
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What equation states that a rigid motion keeps the measure of $ABC$ unchanged?
What equation states that a rigid motion keeps the measure of $ABC$ unchanged?
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$m\angle ABC = m\angle A'B'C'$. Prime notation shows the image after transformation.
$m\angle ABC = m\angle A'B'C'$. Prime notation shows the image after transformation.
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Which option is always true after a rigid motion: $m\angle 1 = m\angle 1'$ or $m\angle 1 > m\angle 1'$?
Which option is always true after a rigid motion: $m\angle 1 = m\angle 1'$ or $m\angle 1 > m\angle 1'$?
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$m\angle 1 = m\angle 1'$. Rigid motions always preserve angle measures.
$m\angle 1 = m\angle 1'$. Rigid motions always preserve angle measures.
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Identify the transformation type: “Slide every point the same distance and direction.”
Identify the transformation type: “Slide every point the same distance and direction.”
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Translation. Key phrase "same distance and direction" identifies translations.
Translation. Key phrase "same distance and direction" identifies translations.
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Identify the transformation type: “Turn a figure around a fixed point by a given degree.”
Identify the transformation type: “Turn a figure around a fixed point by a given degree.”
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Rotation. "Turn around a point" describes rotational motion.
Rotation. "Turn around a point" describes rotational motion.
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Identify the transformation type: “Flip a figure across a line to make a mirror image.”
Identify the transformation type: “Flip a figure across a line to make a mirror image.”
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Reflection. "Mirror image" is the defining feature of reflections.
Reflection. "Mirror image" is the defining feature of reflections.
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What is the image angle measure if $m\angle A = 35^\circ$ and $A$ is translated?
What is the image angle measure if $m\angle A = 35^\circ$ and $A$ is translated?
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$35^\circ$. Translations preserve all angle measures.
$35^\circ$. Translations preserve all angle measures.
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What is the image angle measure if $m\angle B = 118^\circ$ and $B$ is rotated $90^\circ$?
What is the image angle measure if $m\angle B = 118^\circ$ and $B$ is rotated $90^\circ$?
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$118^\circ$. Rotation angle doesn't affect the measure of angles in the figure.
$118^\circ$. Rotation angle doesn't affect the measure of angles in the figure.
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What is the image angle measure if $m\angle C = 62^\circ$ and $C$ is reflected across a line?
What is the image angle measure if $m\angle C = 62^\circ$ and $C$ is reflected across a line?
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$62^\circ$. Reflections preserve angle measures as rigid motions.
$62^\circ$. Reflections preserve angle measures as rigid motions.
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If $m\angle D = 2x + 10$ and after a rotation $m\angle D' = 50$, what is $x$?
If $m\angle D = 2x + 10$ and after a rotation $m\angle D' = 50$, what is $x$?
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$x = 20$. Set $2x + 10 = 50$ since rigid motions preserve angles.
$x = 20$. Set $2x + 10 = 50$ since rigid motions preserve angles.
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If $m\angle E = 5y - 15$ and after a translation $m\angle E' = 70$, what is $y$?
If $m\angle E = 5y - 15$ and after a translation $m\angle E' = 70$, what is $y$?
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$y = 17$. Set $5y - 15 = 70$ since translations preserve angles.
$y = 17$. Set $5y - 15 = 70$ since translations preserve angles.
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If $m\angle F = 3x$ and after a reflection $m\angle F' = 72$, what is $x$?
If $m\angle F = 3x$ and after a reflection $m\angle F' = 72$, what is $x$?
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$x = 24$. Set $3x = 72$ since reflections preserve angle measures.
$x = 24$. Set $3x = 72$ since reflections preserve angle measures.
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Find the missing image measure: $m\angle G = 41^\circ$ and $m\angle G' = ;?$ after any rigid motion.
Find the missing image measure: $m\angle G = 41^\circ$ and $m\angle G' = ;?$ after any rigid motion.
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$41^\circ$. All rigid motions preserve angle measures.
$41^\circ$. All rigid motions preserve angle measures.
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Choose the correct statement about angle measure under rigid motions: preserved or changed?
Choose the correct statement about angle measure under rigid motions: preserved or changed?
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Preserved (unchanged). Rigid motions are distance and angle preserving.
Preserved (unchanged). Rigid motions are distance and angle preserving.
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Find and correct the false claim: “A reflection changes an angle’s measure.” What is the correction?
Find and correct the false claim: “A reflection changes an angle’s measure.” What is the correction?
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Correct: A reflection preserves an angle’s measure. Reflections are rigid motions that preserve angles.
Correct: A reflection preserves an angle’s measure. Reflections are rigid motions that preserve angles.
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Which option is always true for rigid motions: $m\angle A = m\angle A'$, $m\angle A = m\angle A' + 10$, or $m\angle A = 2m\angle A'$?
Which option is always true for rigid motions: $m\angle A = m\angle A'$, $m\angle A = m\angle A' + 10$, or $m\angle A = 2m\angle A'$?
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$m\angle A = m\angle A'$. Only equal measures satisfy the rigid motion property.
$m\angle A = m\angle A'$. Only equal measures satisfy the rigid motion property.
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What is $m\angle C$ if a reflection maps $ C$ to $ C'$ and $m\angle C' = 110^\circ$?
What is $m\angle C$ if a reflection maps $ C$ to $ C'$ and $m\angle C' = 110^\circ$?
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$110^\circ$. Reflections preserve angle measure, so they're equal.
$110^\circ$. Reflections preserve angle measure, so they're equal.
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What is the image measure if $m\angle C = 90^\circ$ and $ C$ is translated to $ C'$?
What is the image measure if $m\angle C = 90^\circ$ and $ C$ is translated to $ C'$?
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$90^\circ$. Translations preserve angle measures exactly.
$90^\circ$. Translations preserve angle measures exactly.
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What is the image measure if $m\angle A = 47^\circ$ and $ A$ is rotated to $ A'$?
What is the image measure if $m\angle A = 47^\circ$ and $ A$ is rotated to $ A'$?
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$47^\circ$. Rotations preserve angle measures exactly.
$47^\circ$. Rotations preserve angle measures exactly.
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What is the image measure if $m\angle B = 122^\circ$ and $ B$ is reflected to $ B'$?
What is the image measure if $m\angle B = 122^\circ$ and $ B$ is reflected to $ B'$?
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$122^\circ$. Reflections preserve angle measures exactly.
$122^\circ$. Reflections preserve angle measures exactly.
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Identify the error: A student says a reflection changes angle measure because it flips the figure. What is the correction?
Identify the error: A student says a reflection changes angle measure because it flips the figure. What is the correction?
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Reflection flips orientation but preserves angle measure; angles stay congruent. Orientation changes, but measures remain equal.
Reflection flips orientation but preserves angle measure; angles stay congruent. Orientation changes, but measures remain equal.
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What is $m\angle B'$ if a translation maps $ B$ to $ B'$ and $m\angle B = 2x$ with $x=34$?
What is $m\angle B'$ if a translation maps $ B$ to $ B'$ and $m\angle B = 2x$ with $x=34$?
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$68^\circ$. Substitute: $m\angle B = 2(34) = 68°$, which equals $m\angle B'$.
$68^\circ$. Substitute: $m\angle B = 2(34) = 68°$, which equals $m\angle B'$.
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What must be true about an angle and its image after a reflection?
What must be true about an angle and its image after a reflection?
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The angle measure stays the same; the image angle is congruent. Reflections flip figures across a line, preserving angle measures.
The angle measure stays the same; the image angle is congruent. Reflections flip figures across a line, preserving angle measures.
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What is the best conclusion: If $ A$ maps to $ A'$ by a rigid motion, then $ A$ and $ A'$ are what?
What is the best conclusion: If $ A$ maps to $ A'$ by a rigid motion, then $ A$ and $ A'$ are what?
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Congruent angles. Equal angle measures mean the angles are congruent.
Congruent angles. Equal angle measures mean the angles are congruent.
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What is the angle-measure rule for a rigid motion (translation, rotation, or reflection)?
What is the angle-measure rule for a rigid motion (translation, rotation, or reflection)?
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A rigid motion preserves angle measure: corresponding angles are congruent. Rigid motions preserve distances and angles, not just positions.
A rigid motion preserves angle measure: corresponding angles are congruent. Rigid motions preserve distances and angles, not just positions.
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