True or False:
a. A rhombus is a parallelogram with four congruent sides.

b. A rectangle is a parallelogra...

Question

True or False:
a. A rhombus is a parallelogram with four congruent sides.

b. A rectangle is a parallelogram with four right angles.

c. A square is a rectangle and a rhombus.

d. A rhombus is always a square.

e. Every parallelogram is a regular quadrilateral.

f. In a rectangle, the diagonals are perpendicular.

CramX · Accepted Answer

Step 1: I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:. Step 2: : Analyze the definition of a rhombus. A rhombus is a quadrilateral with four congruent sides. This means all sides are equal in length, but the angles do not need to be right angles. Step 3: : Evaluate statement a. This is TRUE. A rhombus is defined as a parallelogram where all four sides are equal in length. Step 4: : Evaluate statement b. This is TRUE. A rectangle has four 90-degree angles and opposite sides are parallel. Step 5: : Evaluate statement c. This is TRUE. A square has: - Four right angles (like a rectangle) - Four equal sides (like a rhombus) - Therefore, it satisfies both conditions Step 6: : Evaluate statement d. This is FALSE. A rhombus has four equal sides, but its angles are not necessarily right angles. Only when all angles are 90 degrees does a rhombus become a square. Step 7: : Evaluate statement e. This is FALSE. A regular quadrilateral must have both equal sides and equal angles. A general parallelogram does not meet this condition. Step 8: : Evaluate statement f. This is FALSE. In a rectangle, the diagonals are equal in length but not perpendicular. Final Answer: a. TRUE b. TRUE c. TRUE d. FALSE e. FALSE f. FALSE

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Answer

Full Solution Locked

Step 1:
I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:

Step 2:
: Analyze the definition of a rhombus

Step 3:
: Evaluate statement a

Final Answer

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