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:
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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. -
This parallelogram has 2 pairs of parallel sides.
True – By definition, a parallelogram is a quadrilateral with two pairs of parallel sides. -
This parallelogram is a quadrilateral.
True – A parallelogram is a type of quadrilateral, meaning it has four sides. -
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:
- How do you prove that the triangles formed by the diagonal of a parallelogram are congruent?
- What are the properties of a parallelogram in terms of angles and sides?
- How does a parallelogram differ from a rectangle and a rhombus?
- Can all quadrilaterals be decomposed into two congruent triangles?
- 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
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