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Questions and Answers
What is a rectangle?
What is a rectangle?
- A parallelogram with two right angles
- A rectangle with no equal sides
- A parallelogram with four right angles (correct)
- A parallelogram with all sides equal
What is a rhombus?
What is a rhombus?
A parallelogram with all sides equal.
What defines a square?
What defines a square?
A rectangle with all sides equal and four right angles.
What does Theorem 4-20 state?
What does Theorem 4-20 state?
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What does Theorem 4-21 state?
What does Theorem 4-21 state?
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What does Theorem 4-22 state?
What does Theorem 4-22 state?
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Match the vocabulary word with the correct definition:
Match the vocabulary word with the correct definition:
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Match the reasons with the statements for proving Theorem 4-22:
Match the reasons with the statements for proving Theorem 4-22:
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Study Notes
Rectangles and Related Concepts
- A rectangle is defined as a parallelogram with four right angles.
- A rhombus is a type of parallelogram where all sides are equal in length.
- A square is both a rectangle and a rhombus, characterized by having all sides equal and four right angles.
Key Theorems
- Theorem 4-20: The diagonals of a rectangle are equal in length.
- Theorem 4-21: The diagonals of a rhombus intersect at right angles (are perpendicular).
- Theorem 4-22: Each diagonal of a rhombus bisects the two angles at its vertices.
Vocabulary Matching
- Rectangle: A parallelogram with four right angles.
- Rhombus: A parallelogram with all sides equal.
- Square: A rectangle with all sides equal and all angles being right angles.
Proof Structure for Theorem 4-22
- Given: ABCD is a rhombus.
- To Prove: Diagonal DB bisects angles ABC and ADC.
- Steps to proof:
- Establish triangles ADB and CDB as congruent.
- Conclude that angles ∠1 equals ∠2 and ∠3 equals ∠4.
- Hence, diagonal DB bisects angles ∠ABC and ∠ADC using congruent triangles and the definition of angle bisectors.
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