Podcast
Questions and Answers
Which of the following shapes have all sides congruent?
Which of the following shapes have all sides congruent?
- Trapezoid
- Square (correct)
- Rectangle
- Rhombus (correct)
A rhombus and a kite have diagonals that are perpendicular.
A rhombus and a kite have diagonals that are perpendicular.
True (A)
What is a characteristic of a rhombus related to its diagonals?
What is a characteristic of a rhombus related to its diagonals?
Diagonals bisect opposite angles
What is a defining feature of a square?
What is a defining feature of a square?
What characteristic do rectangles have regarding their diagonals?
What characteristic do rectangles have regarding their diagonals?
A trapezoid has two pairs of parallel sides.
A trapezoid has two pairs of parallel sides.
In a trapezoid, the legs are not parallel.
In a trapezoid, the legs are not parallel.
What is a defining feature of isosceles trapezoids regarding base angles?
What is a defining feature of isosceles trapezoids regarding base angles?
What characteristic do isosceles trapezoids have about their legs?
What characteristic do isosceles trapezoids have about their legs?
All angles in a rectangle are 90 degrees.
All angles in a rectangle are 90 degrees.
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Study Notes
Shape Classifications in Geometry
-
Rhombus and Square
- All sides are congruent, meaning each side is of equal length.
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Rhombus and Kite
- Diagonals intersect at right angles, indicating they are perpendicular to each other.
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Rhombus
- Diagonals bisect the opposite angles, dividing each angle into two equal parts.
-
Square
- All angles are congruent, specifically each angle measures 90 degrees, making it a special case of both a rectangle and rhombus.
-
Rectangle
- Diagonals are congruent, meaning they are of equal length.
-
Trapezoid
- Characterized by having one pair of parallel sides, defining its basic structure.
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Trapezoid (additional definition)
- Legs are not parallel, distinguishing it from isosceles trapezoids, where legs are equal.
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Isosceles Trapezoid
- Each pair of base angles are congruent, ensuring symmetry in the shape.
-
Isosceles Trapezoid (additional definition)
- Legs are congruent in length, further emphasizing its symmetrical properties.
-
Rectangle (additional fact)
- All angles are right angles (90 degrees), reinforcing its classification as a type of quadrilateral.
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