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9-12 Geometry Unit 2 Lesson 13

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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

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.

Problem 2

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

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

Problem 3

ForLesson 12: Proofs about Quadrilaterals

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>

Problem 4

ForLesson 12: Proofs about Quadrilaterals

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.

Problem 5

ForLesson 11: Side-Side-Angle (Sometimes) Congruence

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>

Problem 6

ForLesson 10: Practicing Proofs

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 .

Problem 7

ForLesson 5: Points, Segments, and Zigzags

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.

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 .