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9-12 Integrated Math 2 Unit 1 Lesson 13

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K-5 Math 6-8 Math •9-12 Math

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Integrated Math 1 •Integrated Math 2 Integrated Math 3

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

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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

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Lesson 13
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Unit 1, Lesson 13

Proofs about Parallelograms

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Integrated Math 2

Practice

Problem 1
Student Task Statement
Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram.

Draw a diagram of the situation.

Mark the given information.

Restate the conjecture as a specific statement using the diagram.
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Problem 2

Student Task Statement

In quadrilateral , is congruent to , and is parallel to . Show that is a parallelogram.

<p>Quadrilateral ABCD with line segment AC.</p>

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Problem 3

ForLesson 12: Proofs about Quadrilaterals

Student Task Statement

is an isosceles trapezoid. Name one pair of congruent triangles that could be used to show that the diagonals of an isosceles trapezoid are congruent.

<p>Isosceles trapezoid A B D E. Angles are marked with tick marks, as follows: D E A, one mark; E A B, two marks; A B D, two tick marks; B D E, one tick mark. Segment A E and B D each have one tick mark.<br>
</p>

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Problem 4

ForLesson 12: Proofs about Quadrilaterals

Student Task Statement

Select the conjecture with the rephrased statement of proof to show that the diagonals of a parallelogram bisect each other.

<p>Quadrilateral EFGH. Line segments EG and HF intersect at point K.</p>

In parallelogram , show triangle is congruent to triangle .
In parallelogram , show triangle is congruent to triangle .
In parallelogram , show is congruent to and is congruent to .
In quadrilateral with congruent to and congruent to , show is a parallelogram.

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Problem 5

ForLesson 12: Proofs about Quadrilaterals

Student Task Statement

Priya is convinced the diagonals of the isosceles trapezoid are congruent. She knows that if she can prove triangles that include the diagonals congruent, then she will show that diagonals are also congruent. Help her complete the proof.

is an isosceles trapezoid.

<p>Isosceles trapezoid A B D E. Angles are marked with tick marks, as follows: D E A, one mark; E A B, two marks; A B D, two tick marks; B D E, one tick mark. Segment A E and B D each have one tick mark.<br>
</p>

Draw auxiliary lines that are diagonals and . is congruent to because they are the same segment. We know angle and are congruent. We know is congruent to . Therefore, triangle and are congruent because of . Finally, diagonal is congruent to because .

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Problem 6

ForLesson 4: Big Angles, Long Sides. Small Angles, Short Sides.

Student Task Statement

List the side lengths in order from least to greatest.

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Lesson 13 Resources

Student Materials