Questions and Answers
What is a rectangle?
What is a rhombus?
A parallelogram with all sides equal.
What defines a square?
A rectangle with all sides equal and four right angles.
What does Theorem 4-20 state?
Signup and view all the answers
What does Theorem 4-21 state?
Signup and view all the answers
What does Theorem 4-22 state?
Signup and view all the answers
Match the vocabulary word with the correct definition:
Signup and view all the answers
Match the reasons with the statements for proving Theorem 4-22:
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on parallelograms, specifically rectangles, rhombuses, and squares. This quiz will cover key definitions and theorems related to these shapes to help reinforce your understanding. Perfect for geometry students looking to refresh their skills on these fundamental concepts.
