Two rectangles $ABCD$ABCD and $A'B'C'D'$A′B′C′D′ are plotted on a Cartesian plane. In rectangle $ABCD$ABCD, $AB$AB is the left side, $CD$CD is the right side, $BC$BC is the top side, and $AD$AD is the bottom side. In rectangle $A'B'C'D'$A′B′C′D′, $A'$A′ is the left side, $C'$C′ is the right side, $B'$B′ is the top side, and $A'$A′ is the bottom side. The coordinates of the vertices of rectangle $ABCD$ABCD are $\left(-1,-2\right)$(−1,−2) for $A$A, $\left(-1,1\right)$(−1,1) for $B$B, $\left(2,1\right)$(2,1) for $C$C, and $\left(2,-2\right)$(2,−2) for $D$D. The coordinates of the vertices of rectangle $A'B'C'D'$A′B′C′D′ are $\left(-2,-4\right)$(−2,−4) for $A'$A′, $\left(-2,2\right)$(−2,2) for $B'$B′, $\left(4,2\right)$(4,2) for $C'$C′, and $\left(4,-4\right)$(4,−4) for $D'$D′. The coordinates of the vertices are not explicitly labeled on the graph.

Are the two rectangles similar, congruent or neither?

Congruent

Similar

Neither

What is the transformation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?

Rotation

Translation

Dilation

Reflection

What is the scale factor of the dilation from rectangle $ABCD$ABCD to rectangle $A'B'C'D'$A′B′C′D′?

Easy

< 1min

Consider the triangle with vertices at $A$A$\left(-3,-2\right)$(−3,−2), $B$B$\left(2,1\right)$(2,1) and $C$C$\left(3,-3\right)$(3,−3), and the triangle with vertices at $A'$A′$\left(-9,-6\right)$(−9,−6), $B'$B′$\left(6,3\right)$(6,3) and $C'$C′$\left(9,-9\right)$(9,−9).

Easy

< 1min

Consider the quadrilateral with vertices at $A$A$\left(-3,-3\right)$(−3,−3), $B$B$\left(-3,3\right)$(−3,3), $C$C$\left(3,3\right)$(3,3) and $D$D$\left(3,-3\right)$(3,−3), and the quadrilateral with vertices at $A'$A′$\left(-9,-9\right)$(−9,−9), $B'$B′$\left(-9,9\right)$(−9,9), $C'$C′$\left(9,9\right)$(9,9) and $D'$D′$\left(9,-9\right)$(9,−9).

Easy

< 1min

Consider a transformation that causes one vertex of a triangle to move from $\left(x,y\right)$(x,y) to $\left(0.6x,0.6y\right)$(0.6x,0.6y).

Easy

< 1min

Outcomes

9.G.T.1

Two triangles are congruent if any two sides and the included angle of one triangle is equal to any two sides and the included angle of the other triangle (SAS Congruence). Two triangles are congruent if any two angles and the included side of one triangle is equal to any two angles and the included side of the other triangle (ASA Congruence). Two triangles are congruent if the three sides of one triangle are equal to three sides of the other triangle (SSS Congruence).

Transformations and Similarity

Interactive practice questions

Outcomes

9.G.T.1

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