Task Sets: Angles are taken to angles of the same measure - Common Core Math - Grade 8

Recall / Warm-Up

These problems review skills you already know: classifying angles, naming rigid motions, and applying transformation rules.

An angle measures $118\degree$ . How is this angle classified?

Acute

Right

Obtuse

Straight

Which list contains only rigid motions (transformations that keep a figure the same size and shape)?

Translation, reflection, rotation

Translation, dilation, rotation

Dilation, reflection, stretch

Rotation, stretch, dilation

$A coordinate grid showing an angle with vertex B at (2, 1) and a dashed arrow indicating a translation.$

Apply the translation rule $(x, y) \rightarrow (x + 3, y + 2)$ to the vertex of an angle located at $(2, 1)$ . What is the x-coordinate of the image vertex?

Fluency Practice

Apply each transformation and verify the angle-preservation property. Use the measure of the original angle to predict the measure of the image.

$A coordinate grid showing a 55-degree angle and its translated image angle of the same shape.$

Angle $ABC$ measures $55\degree$ . It is translated by the rule $(x, y) \rightarrow (x + 4, y + 3)$ to form image angle $A'B'C'$ . What is the measure of the image angle?

$55\degree$

$59\degree$ , because the translation adds to the measure.

$62\degree$ , because both shifts add to the measure.

It cannot be determined without measuring.

An obtuse angle measuring $105\degree$ is translated by the rule $(x, y) \rightarrow (x - 2, y + 4)$ . What is the measure of the image angle, in degrees?

$A coordinate grid showing a 72-degree angle on the right and its reflection across the y-axis on the left.$

Angle $GHI$ measures $72\degree$ . It is reflected across the y-axis by the rule $(x, y) \rightarrow (-x, y)$ . The image angle opens in the opposite direction. What is the measure of the image angle, in degrees?

$A coordinate grid showing a 110-degree angle and its image after a 90-degree counterclockwise rotation about the origin.$

An angle measuring $110\degree$ is rotated $90\degree$ counterclockwise about the origin. What is the measure of the image angle, in degrees?

An angle with the unusual measure of $53\degree$ is reflected across a diagonal line. What is the measure of the image angle, in degrees?

Exercises: Rigid Motions Preserve Angle Measure

Recall / Warm-Up

Fluency Practice