6.01 Congruence transformations

Lesson

Practice

Adaptive

Worksheet

Interactive practice questions

Consider the figures shown.

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Two $quadrilateral$quadrilateral are placed on a Coordinate Plane, where the x- and y- axes are labeled and range from -10 to 10. These $quadrilateral$quadrilateral, $ABCD$ABCD and $A'B'C'D'$A′B′C′D′, have the same shape and size but are situated differently. The coordinates of the vertices are not explicitly given. The vertices of $quadrilateral$quadrilateral $ABCD$ABCD are located at A $\left(3,1\right)$(3,1), B $\left(3,8\right)$(3,8), C $\left(8,8\right)$(8,8), and D $\left(8,1\right)$(8,1). Similarly, the vertices of $quadrilateral$quadrilateral $A'B'C'D'$A′B′C′D′ are positioned at A' $\left(-2,3\right)$(−2,3), B' $\left(-2,10\right)$(−2,10), C' $\left(3,10\right)$(3,10), and D' $\left(3,3\right)$(3,3).

What single transformation can take $quadrilateral$ $ABCD$ABCD to $quadrilateral$ $A'B'C'D'$A′B′C′D′?

Rotation

Translation

Reflection

Dilation

Identify the transformation from $quadrilateral$ $ABCD$ABCD to $quadrilateral$ $A'B'C'D'$A′B′C′D′.

A translation $5$5 units $left$ and $2$2 units $up$ .

A translation $2$2 units $left$ and $5$5 units $up$ .

A translation $5$5 units $right$ and $2$2 units $down$ .

A translation $2$2 units $right$ and $5$5 units $down$ .

Easy

1min

Consider the figures shown.

Easy

1min

Using quadrilateral $A'B'C'D'$A′B′C′D′ as a guide, determine the correct sequence of transformations that maps quadrilateral $ABCD$ABCD to quadrilateral $A''B''C''D''$A′′B′′C′′D′′.

Medium

< 1min

Medium

< 1min

Outcomes

G.RLT.3

The student will solve problems, including contextual problems, involving symmetry and transformation.

G.RLT.3ci

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: i) translations;

G.RLT.3cii

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: ii) reflections over any horizontal or vertical line or the lines y = x or y = -x;

G.RLT.3ciii

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: iii) clockwise or counterclockwise rotations of 90°, 180°, 270°, or 360° on a coordinate grid where the center of rotation is limited to the origin;