# MA.912.GR.1.4 Export Print
Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.

### Clarifications

Clarification 1: Postulates, relationships and theorems include opposite sides are congruent, consecutive angles are supplementary, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and rectangles are parallelograms with congruent diagonals.

Clarification 2: Instruction includes constructing two-column proofs, pictorial proofs, paragraph and narrative proofs, flow chart proofs or informal proofs.

Clarification 3: Instruction focuses on helping a student choose a method they can use reliably.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Geometric Reasoning
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.912.GR.1.AP.4: Use the relationships and theorems about parallelograms. Solve mathematical and/or real-world problems involving postulates, relationships and theorems of parallelograms.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Comparing Lengths in a Parallelogram:

Students are given parallelogram ABCD along with midpoint E of diagonal AC and are asked to determine the relationship between the lengths AE + ED and BE + EC.

Type: Formative Assessment

Finding Angle C:

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measure of an angle opposite one of the given angles.

Type: Formative Assessment

Frame It Up:

Students are asked to explain how to determine whether a four-sided frame is a rectangle using only a tape measure.

Type: Formative Assessment

Two Congruent Triangles:

Students are asked to explain why a pair of triangles formed by the sides and diagonals of a parallelogram are congruent.

Type: Formative Assessment

Angles of a Parallelogram:

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measures of all four angles describing any theorems used.

Type: Formative Assessment

Proving Congruent Diagonals:

Students are asked to prove that the diagonals of a rectangle are congruent.

Type: Formative Assessment

Proving a Rectangle Is a Parallelogram:

Students are asked to prove that a rectangle is a parallelogram.

Type: Formative Assessment

Proving Parallelogram Angle Congruence:

Students are asked to prove that opposite angles of a parallelogram are congruent.

Type: Formative Assessment

Proving Parallelogram Diagonals Bisect:

Students are asked to prove that the diagonals of a parallelogram bisect each other.

Type: Formative Assessment

Proving Parallelogram Side Congruence:

Students are asked to prove that opposite sides of a parallelogram are congruent.

Type: Formative Assessment

Prove Rhombus Diagonals Bisect Angles:

Students are asked to prove a specific diagonal of a rhombus bisects a pair of angles.

Type: Formative Assessment

## MFAS Formative Assessments

Angles of a Parallelogram:

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measures of all four angles describing any theorems used.

Comparing Lengths in a Parallelogram:

Students are given parallelogram ABCD along with midpoint E of diagonal AC and are asked to determine the relationship between the lengths AE + ED and BE + EC.

Finding Angle C:

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measure of an angle opposite one of the given angles.

Frame It Up:

Students are asked to explain how to determine whether a four-sided frame is a rectangle using only a tape measure.

Prove Rhombus Diagonals Bisect Angles:

Students are asked to prove a specific diagonal of a rhombus bisects a pair of angles.

Proving a Rectangle Is a Parallelogram:

Students are asked to prove that a rectangle is a parallelogram.

Proving Congruent Diagonals:

Students are asked to prove that the diagonals of a rectangle are congruent.

Proving Parallelogram Angle Congruence:

Students are asked to prove that opposite angles of a parallelogram are congruent.

Proving Parallelogram Diagonals Bisect:

Students are asked to prove that the diagonals of a parallelogram bisect each other.

Proving Parallelogram Side Congruence:

Students are asked to prove that opposite sides of a parallelogram are congruent.

Two Congruent Triangles:

Students are asked to explain why a pair of triangles formed by the sides and diagonals of a parallelogram are congruent.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.