Navigation

9-12 Integrated Math 2 Unit 1 Lesson 13

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

Unit

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

Modeling Prompts

Lesson

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

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

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

Modeling Prompts

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 | Practice | Loading...

Sign in to access protected content and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

Curriculum

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

Professional Learning

Illustrative Mathematics® has operated as an independent 501(c)3 non-profit organization since 2013.

©2024 Illustrative Mathematics®. Licensed under CC BY-NC 4.0.

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written permission of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses. See the image attribution section for more information.

Settings

Audience

family

Not all roles available for this page.

Assessment Access

Sign in to view assessments and invite other educators

Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.

teacher
student
family

Unit 1, Lesson 13

Proofs about Parallelograms

$Course Icon$

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.

to access Practice Problem Solutions.

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>

to access Practice Problem Solutions.

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>

to access Practice Problem Solutions.

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.

to access Practice Problem Solutions.

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 .

to access Practice Problem Solutions.

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.

to access Practice Problem Solutions.

Lesson 13 Resources

Student Materials