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Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Standard #: MAFS.912.G-CO.3.11Archived Standard

Standard Information

General Information

Subject Area: Mathematics

Grade: 912

Domain-Subdomain: Geometry: Congruence

Cluster: Level 3: Strategic Thinking & Complex Reasoning

Cluster: Prove geometric theorems. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14

Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information

Date of Last Rating: 02/14

Status: State Board Approved - Archived

Assessed: Yes

Related Courses

Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) 1200400
Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) 1206310
Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) 1206320
Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current)) 1206315
Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current)) 7912065

Related Resources

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.
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.
Two Congruent Triangles Students are asked to explain why a pair of triangles formed by the sides and diagonals of a parallelogram are congruent.
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.
Proving Congruent Diagonals Students are asked to prove that the diagonals of a rectangle are congruent.
Proving a Rectangle Is a Parallelogram Students are asked to prove that a rectangle is a parallelogram.
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.

Lesson Plans

To Be or Not to Be a Parallelogram Students apply parallelogram properties and theorems to solve real world problems. The acronym, P.I.E.S. is introduced to support a problem solving strategy, which involves drawing a Picture, highlighting important Information, Estimating and/or writing equation, and Solving problem.
Diagonally Half of Me! This lesson is an exploration activity assisting students prove that diagonals of parallelograms bisect each other. It allows them to compare other quadrilaterals with parallelograms in order to make conjectures about the diagonals of parallelograms.
Proving Parallelograms Algebraically This lesson reviews the definition of a parallelogram and related theorems. Students use these conditions to algebraically prove or disprove a given quadrilateral is a parallelogram.
Evaluating Statements About Length and Area This lesson unit is intended to help you assess how well students can understand the concepts of length and area, use the concept of area in proving why two areas are or are not equal and construct their own examples and counterexamples to help justify or refute conjectures.

Problem-Solving Task

Midpoints of the Side of a Parallelogram This is a reasonably direct task aimed at having students use previously-derived results to learn new facts about parallelograms, as opposed to deriving them from first principles.

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.
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.