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9-12 Geometry Unit 2 Lesson 13

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K-5 Math 6-8 Math •9-12 Math

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Algebra 1 •Geometry Algebra 2 Extra Support Materials for Algebra 1

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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

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Unit 2, Lesson 13

Proofs about Parallelograms

Geometry

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 11: Side-Side-Angle (Sometimes) Congruence

Student Task Statement

Is triangle congruent to triangle ?
Explain your reasoning.

<p>Quadrilateral J H I E. A line connects H and E. Sides J H and H I have single tick marks. Angles J and I are marked with small squares.</p>

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Problem 6

ForLesson 10: Practicing Proofs

Student Task Statement

Select all true statements based on the diagram.

<p>Quadrilateral ABCD. Line AB is parallel to line DC, both cut by congruent transversals AD and BC. Diagonals AC and DB bisect each other at point E at a right angle. Segment AE is congruent to segment BE.</p>

Segment is congruent to segment .

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Problem 7

ForLesson 5: Points, Segments, and Zigzags

Student Task Statement

Which conjecture is possible to prove?

If the four angles in a quadrilateral are congruent to the four angles in another quadrilateral, then the two quadrilaterals are congruent.
If the four sides in a quadrilateral are congruent to the four sides in another quadrilateral, then the two quadrilaterals are congruent.
If the three angles in a triangle are congruent to the three angles in another triangle, then the two triangles are congruent.
If the three sides in a triangle are congruent to the three sides in another triangle, then the two triangles are congruent.

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Lesson 13 Resources

Student Materials

Segment is congruent to segment .

Line is parallel to line .

Line is parallel to line .

Angle is congruent to angle .

Angle is congruent to angle .