QQuestionMathematics
QuestionMathematics
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.
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Answer
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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
\text{Statement a: A rhombus is a parallelogram with four congruent sides.}
This is TRUE. A rhombus is defined as a parallelogram where all four sides are equal in length.
Step 4:: Evaluate statement b
\text{Statement b: A rectangle is a parallelogram with four right angles.}
This is TRUE. A rectangle has four 90 -degree angles and opposite sides are parallel.
Step 5:: Evaluate statement c
\text{Statement c: A square is a rectangle and a rhombus.}
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
\text{Statement d: A rhombus is always a square.}
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
\text{Statement e: Every parallelogram is a regular quadrilateral.}
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
\text{Statement f: In a rectangle, the diagonals are perpendicular.}
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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