QQuestionMathematics
QuestionMathematics
"If the statement is true, explain why. If the statement is false, correct it so that it is true.
a. A kite is sometimes a rhombus.
b. A square is a rhombus.
c. A square is a rectangle.
d. A rectangle is a square."
5 months agoReport content
Answer
Full Solution Locked
Sign in to view the complete step-by-step solution and unlock all study resources.
Step 1I'll go through each statement and determine if it's true or false.
For any false statements, I will correct them to make them true. a. A kite is sometimes a rhombus. A kite is not always a rhombus. However, there is a special type of kite called a rhombus kite, which has all sides equal in length. In general, a kite has two pairs of equal sides but is not necessarily equilateral. So, the statement is false as it is, but it can be corrected to: A kite can be a rhombus if and only if all its sides are equal in length. b. A square is a rhombus. This statement is true because a square has all sides equal in length and all angles equal to 90 degrees, making it both a rectangle and a rhombus. c. A square is a rectangle. This statement is also true because a square has all sides equal in length and all angles equal to 90 degrees, making it a rectangle. d. A rectangle is a square. This statement is false. Although a rectangle has all angles equal to 90 degrees, it does not necessarily have all sides equal in length. The statement can be corrected to: A rectangle is a square if and only if all its sides are equal in length.
Final Answer
a. A kite can be a rhombus if and only if all its sides are equal in length. b. True. c. True. d. A rectangle is a square if and only if all its sides are equal in length.
Need Help with Homework?
Stuck on a difficult problem? We've got you covered:
- Post your question or upload an image
- Get instant step-by-step solutions
- Learn from our AI and community of students