Math Problem Statement

Select all of the statements that are true about the parallelogram. Parallelogram

This parallelogram can be decomposed into two identical triangles.

This parallelogram has 2 pairs of parallel sides.

This parallelogram is a quadrilateral.

This parallelogram has 4 right angles.

Solution

Let's analyze each statement one by one:

  1. This parallelogram can be decomposed into two identical triangles.
    True – A parallelogram can always be divided into two congruent (identical) triangles by drawing one of its diagonals.

  2. This parallelogram has 2 pairs of parallel sides.
    True – By definition, a parallelogram is a quadrilateral with two pairs of parallel sides.

  3. This parallelogram is a quadrilateral.
    True – A parallelogram is a type of quadrilateral, meaning it has four sides.

  4. This parallelogram has 4 right angles.
    False – A parallelogram typically has two pairs of opposite angles that are equal, but not necessarily 90° (right angles). Only a special type of parallelogram, like a rectangle, has 4 right angles.

Summary of True Statements:

  • This parallelogram can be decomposed into two identical triangles.
  • This parallelogram has 2 pairs of parallel sides.
  • This parallelogram is a quadrilateral.

Would you like a detailed explanation of any of these? Here are five related questions for further exploration:

  1. How do you prove that the triangles formed by the diagonal of a parallelogram are congruent?
  2. What are the properties of a parallelogram in terms of angles and sides?
  3. How does a parallelogram differ from a rectangle and a rhombus?
  4. Can all quadrilaterals be decomposed into two congruent triangles?
  5. Why is a rectangle considered a special type of parallelogram?

Tip: The sum of the interior angles of any quadrilateral is always 360 degrees.

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Math Problem Analysis

Mathematical Concepts

Geometry
Parallelograms
Quadrilaterals
Triangles

Formulas

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Theorems

Properties of Parallelograms
Congruent Triangles Theorem

Suitable Grade Level

Grades 6-8