Unit 1, Lesson 14

Congruence for Quadrilaterals

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Integrated Math 2

Practice

Problem 1

ForLesson 13: Proofs about Parallelograms

Student Task Statement

In quadrilateral , is congruent to , and is parallel to . Andre has written a proof to show that is a parallelogram. Fill in the blanks to complete the proof.

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

Since is parallel to , alternate interior angles and are congruent. is congruent to since segments are congruent to themselves. Along with the given information that is congruent to , triangle is congruent to by the Triangle Congruence Theorem. Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle is congruent to . Since those alternate interior angles are congruent, must be parallel to . Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, is a parallelogram.

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Problem 2

ForLesson 13: Proofs about Parallelograms

Student Task Statement

Select the statement that must be true.

Parallelograms have at least one right angle.
If a quadrilateral has opposite sides that are both congruent and parallel, then it is a parallelogram.
Parallelograms have congruent diagonals.
The height of a parallelogram is greater than the lengths of the sides.

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Problem 3

ForLesson 12: Proofs about Quadrilaterals

Student Task Statement

is a parallelogram, and angle is a right angle. Select all statements that must be true.

<p>Quadrilateral EFGH with angle HEF as a right angle. Line segments EG and HF intersect at point D.</p>

is a rectangle.

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Problem 4

ForLesson 13: Proofs about Parallelograms

Student Task Statement

is an isosceles trapezoid. Priya makes a claim that triangle is congruent to triangle . Convince Priya this is not true.

<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 5

ForLesson 13: Proofs about Parallelograms

Student Task Statement

In quadrilateral , triangle is congruent to . Show that is a parallelogram.

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Triangle is congruent to triangle .

is congruent to , , and .

Triangle is congruent to triangle .

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Congruence for Quadrilaterals

Practice

Problem 1

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Problem 2

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Problem 3

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Problem 4

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Problem 5

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Lesson 14 Resources