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6-8 Accelerated 7 Unit 1 Lesson 11

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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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 Lesson 18

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 1, Lesson 11

Congruence

Accelerated 7

Practice

Problem 1

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 \(ABCDE\) and the angle measures of pentagon \(FGHIJ\).

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Lesson 11 Resources

Student Materials

Problem 2

These two figures are congruent and have corresponding points marked.

Transformation quadrilaterals.

Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
Measure angles \(ABC\) and \(A’B’C’\) to check your answer.

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Problem 3

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 4

Which of these four figures is congruent to this figure?

A parallelogram with three blue dots on the inside.

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