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6-8 Grade 8 Unit 1 Lesson 12

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K-5 Math •6-8 Math 9-12 Math

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Grade 6 Grade 7 •Grade 8

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 •Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17

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Unit 1, Lesson 12

Congruent Polygons

Grade 8

Practice

Problem 1
Student Task Statement
Show that the two pentagons in the following image are congruent.

Two figures A B C D E and F G H I J on a square grid. Let the lower left corner be (0 comma 0). Then A B C D E has coordinates A(2 comma 3), B(1 comma 5), C(2 comma 6), D(5 comma 5) and E(4 comma 1) and F G H I J has coordinates F(7 comma 3), G(11 comma 2), H(12 comma 5), I(11 comma 6) and J(9 comma 5). For figure A B C D E, angle A is 162 degrees, angle B is 108 degree, angle C is 117 degrees, angle D is 94 degrees and angle E is 59 degrees. For figure F G H I J, side F G is 4 point 1, side G H is 3 point 2, side H I is 1 point 4, side I J is 2 point 2 and side J F is 2 point 8. Figure J I H G F appears to be the image of figure A B C D E after a rotation and a translation.

Find the side lengths of pentagon and the angle measures of pentagon .

Lesson 12 Resources

Student Materials Student Materials in Spanish

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Problem 2

Student Task Statement

For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.

Two quadrilaterals A B C D and E F G H on a square grid. Let the lower left corner be (0 comma 0). Then the coordinates of A B C D are A(1 comma 3), B(2 comma 4), C(2 comma 5)and D(5 comma 5). The coordinates of E F G H are E(11 comma 1), F(10 comma 2), G(10 comma 3)and H(6 comma 3).
Two figures A B C D E F and G H I J K L on a coordinate plane, origin O. Horizontal axis scale negative 7 to 6 by 1’s. Vertical axis scale negative 3 to 4 by 1’s. The coordinates of A B C D E F are A(negative 6 comma 2), B(negative 4 comma 2), C(negative 4 comma negative 2 ), D(negative 2 comma 3), E(negative 4 comma 4) and F(negative 7 comma 4 ). The coordinates of G H I J K L are G(0 comma negative 1), H(5 comma negative 3), I(6 comma negative1), J(6 comma 2), K(4 comma 1) and L(4 comma 0).
Two circles A and C on a coordinate plane, origin O. Horizontal axis scale negative 8 to 7 by 1’s. Vertical axis scale negative 4 to 5 by 1’s. The center of circle A is A(negative 4 comma 2). The center of circle C is C(4 comma negative 1). Both circles have a diameter of 2.

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Problem 3

ForLesson 8: Rotation Patterns

Student Task Statement

Draw segment .
When is rotated around point , the resulting segment is the same as . Where could point be located?

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Problem 4

ForLesson 10: Composing Figures

Student Task Statement

Here is a trapezoid.

Trapezoid <span class="math" data-png-file-id="11020">\(A\ B\ C\ D\)</span>. Upper and lower sides are parallel. Upper and lower left angles are right angles. Upper right angle is 120 degrees and lower right angle is 60 degrees.

Using rigid transformations on the trapezoid, build a pattern. Describe some of the rigid transformations you used.

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