Question

transformations: (rigid motion) date:______
classwork
tell whether the transformation appears to be a rigid motion. explain. (5 points each)

1. 2.

preimage image preimage image

1. identify the type of transformation. 4.identify the type of transformation.

what is the image of segment fg? what is the image of angle j?

1. (10 points)

for each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box.

Explanation:

1. Rigid Motion Check

• Step1: Analyze Side - Length and Angle Preservation

A rigid motion (isometry) preserves side - lengths and angles. For the first pair of triangles, since the transformation does not change the shape and size (side - lengths and angles are preserved), it is a rigid motion.

• Step2: Analyze the Second Pair (Trapezoids)

The second pair of trapezoids also has no change in side - lengths and angles, so it is a rigid motion.

3. Transformation Type and Image of Segment

• Step1: Identify Transformation Type

Looking at the triangle \(FGH\) and its image \(F'G'H\), since the figure is rotated around point \(H\), the transformation is a rotation.

• Step2: Find the Image of Segment \(FG\)

In a rotation, the image of segment \(FG\) is segment \(F'G'\).

4. Transformation Type and Image of Angle

• Step1: Identify Transformation Type

The transformation from the larger quadrilateral \(JLKI\) to the smaller quadrilateral \(J'L'K'I\) is a dilation (a similarity transformation that changes the size but not the shape).

• Step2: Find the Image of Angle \(J\)

In a dilation, the image of angle \(J\) is angle \(J'\) (because dilations preserve angle measures).

4. Properties of Transformations

• Translation
• Step1: Congruence Check

Translation is a rigid motion. So, the image and pre - image are congruent.

• Step2: Length and Angle Preservation

Since it is a rigid motion, lengths of segments and measures of angles are preserved.

• Reflection
• Step1: Congruence Check

Reflection is a rigid motion. So, the image and pre - image are congruent.

• Step2: Length and Angle Preservation

Since it is a rigid motion, lengths of segments and measures of angles are preserved.

• Rotation
• Step1: Congruence Check

Rotation is a rigid motion. So, the image and pre - image are congruent.

• Step2: Length and Angle Preservation

Since it is a rigid motion, lengths of segments and measures of angles are preserved.

• Dilation
• Step1: Congruence Check

Dilation is a similarity transformation. The image and pre - image are similar (but not congruent if the scale factor is not \(1\)).

• Step2: Length and Angle Preservation

Dilation preserves angle measures (because the shape is the same), but changes the lengths of segments (by the scale factor).

Answer:

1. Yes, it is a rigid motion (preserves side - lengths and angles).
2. Yes, it is a rigid motion (preserves side - lengths and angles).
3. Rotation; \(F'G'\)
4. Dilation; \(J'\)

4.

Transformation	The image and pre - image are congruent	The image and pre - image are similar but not congruent	Lengths of segments are preserved	Measures of angles are preserved
Reflection	\(\checkmark\)	\(\)	\(\checkmark\)	\(\checkmark\)
Rotation	\(\checkmark\)	\(\)	\(\checkmark\)	\(\checkmark\)
Dilation	\(\)	\(\checkmark\)	\(\)	\(\checkmark\)