Topics
3. Geometry
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United States of AmericaFL
Grade 8

3.04 Congruence transformations

Lesson
Worksheet
Practice
Worksheet
Congruence transformations
1

Consider the figures shown on the coordinate plane:

a

Are the two shapes similar, congruent or neither?

b

Describe a transformation that could transform one quadrilateral to the other.

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2

Consider the following diagram:

a

Describe the translations required to move point X to point B.

b

Using this translation, which points of \triangle ABC will point Y and point Z translate to?

c

Are \triangle ABC and \triangle YXZ congruent?

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3

Consider the following diagram:

a

Describe the translations required to move X to A.

b

Now, which points of \triangle ABC will Y and Z translate to?

c

Are \triangle ABC and \triangle XYZ congruent?

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4

In the diagram shown, X is a translation of C, and Y is a translation of A:

Plot Z on the given coordinate plane so that the resulting \triangle YZX is congruent to \triangle A B C.

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5

Consider the two triangles drawn in the following diagram.

Are \triangle Y B C and \triangle Y X Z congruent?

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6

Consider the two triangles drawn in the diagram shown.

Are \triangle X B C and \triangle X Y Z congruent? Explain your answer.

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7

Consider the two triangles drawn in the diagram below.

Are \triangle A B C and \triangle XZY congruent? Explain your answer.

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8

For each of the following pairs of quadrilaterals:

i

State whether the two quadrilaterals are similar, congruent or neither.

ii

State the single type of transformation required to transform quadrilateral ABCD into quadrilateral A'B'C'D'.

iii

State a series of transformations that could transform quadrilateral ABCD into quadrilateral A'B'C'D'.

a
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b

A quadrilateral with vertices at A(2, 1),\, B(2, 9),\, C(8, 9), and D(8, 1), and another quadrilateral with vertices at A'(1, -2),\, B'(9, -2),\, C'(9, -8), and D'(1, -8).

c

A quadrilateral with vertices at A(3, -1), B(1, -8), C(5, -8)and D(7, -1), and the quadrilateral with vertices at A'(-3, -1), B'(-1, -8), C'(-5, -8) and D'(-7, -1).

9

For each of the following pairs of triangles:

i

State whether the two triangles similar, congruent or neither.

ii

State the single type of transformation required to transform \triangle ABC into \triangle A'B'C'.

iii

State the transformation or series of transformations that could transform \triangle ABC into \triangle A'B'C'.

a
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b
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c

A triangle with vertices at A(-4, -1),\, B(1, 3), and C(2, -3), and another triangle with vertices at A'(0, -3),\, B'(5, 1), and C'(6, -5).

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Outcomes

MA.8.GR.2.1

Given a preimage and image generated by a single transformation, identify the transformation that describes the relationship.

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