All flashcards
Flashcard 1: Which quadrilateral must have diagonals that are perpendicular?
Answer: Rhombus. Rhombuses feature perpendicular diagonals as a result of all sides being equal, forming right angles at the intersection.
Flashcard 2: Which classification is guaranteed if a quadrilateral has exactly one pair of parallel sides and congruent legs?
Answer: Isosceles trapezoid. Congruent legs in a trapezoid with one pair of parallel sides ensure base angles are equal, classifying it as isosceles.
Flashcard 3: Which condition is sufficient to prove a quadrilateral is a parallelogram using diagonals?
Answer: The diagonals bisect each other. Diagonals bisecting each other indicate midpoints coincide, proving opposite sides parallel and equal for a parallelogram.
Flashcard 4: Which condition is sufficient to prove a quadrilateral is a parallelogram using angles?
Answer: Both pairs of opposite angles are congruent. Congruent opposite angles imply a parallelogram because consecutive angles would then be supplementary, forcing parallel sides.
Flashcard 5: Which condition is sufficient to prove a quadrilateral is a parallelogram?
Answer: Both pairs of opposite sides are congruent. If both pairs of opposite sides are congruent, the quadrilateral must be a parallelogram by the converse of the opposite sides theorem.
Flashcard 6: Which quadrilateral must have diagonals where one diagonal bisects the other?
Answer: Kite. In kites, the diagonal between the equal sides bisects the other diagonal due to the symmetry of adjacent congruent sides.
Flashcard 7: Which quadrilateral must have diagonals that are perpendicular and congruent?
Answer: Square. Squares possess both perpendicular diagonals from rhombus properties and congruent diagonals from rectangle properties.
Flashcard 8: Which quadrilateral must have diagonals that are congruent (same length)?
Answer: Rectangle. Rectangles have congruent diagonals because their right angles and equal opposite sides apply the Pythagorean theorem equally.
Flashcard 9: Which quadrilateral must have diagonals that bisect each other?
Answer: Parallelogram. In parallelograms, diagonals always bisect each other due to the parallel opposite sides creating equal triangles.
Flashcard 10: What is the definition of a square using both sides and angles?
Answer: A quadrilateral with 4 congruent sides and 4 right angles. Squares combine properties of rectangles and rhombuses, with equal sides and right angles for full symmetry.
Flashcard 11: What is the definition of a rhombus using side lengths?
Answer: A parallelogram with 4 congruent sides. Rhombuses are parallelograms with all sides equal, resulting in perpendicular diagonals that bisect each other.
Flashcard 12: What is the definition of a rectangle using angles?
Answer: A parallelogram with 4 right angles. Rectangles are parallelograms where all angles are 90circ, ensuring congruent diagonals.
Flashcard 13: What is the definition of a kite using congruent sides?
Answer: A quadrilateral with two pairs of adjacent congruent sides. Kites feature two pairs of adjacent equal sides, leading to perpendicular diagonals where one bisects the other.
Flashcard 14: What is the definition of an isosceles trapezoid using legs and angles?
Answer: A trapezoid with congruent legs (and congruent base angles). Isosceles trapezoids have non-parallel sides (legs) of equal length, resulting in equal base angles for symmetry.
Flashcard 15: What is the definition of a trapezoid on the ISEE using parallel sides?
Answer: A quadrilateral with at least one pair of parallel sides. On the ISEE, trapezoids are defined inclusively with at least one pair of parallel sides, allowing for various subtypes.
Flashcard 16: What is the definition of a parallelogram using side relationships?
Answer: A quadrilateral with both pairs of opposite sides parallel. Parallelograms require both pairs of opposite sides to be parallel, ensuring opposite sides are also equal in length.
Flashcard 17: What is the definition of a quadrilateral?
Answer: A polygon with 4 sides. Quadrilaterals are classified as polygons with exactly four sides, forming the basis for further subclassifications.
Flashcard 18: What is the definition of a polygon in terms of sides and edges?
Answer: A closed figure made of straight line segments. Polygons are defined as closed plane figures bounded by straight line segments, distinguishing them from open or curved shapes.
Flashcard 19: Which option is always true: If a quadrilateral is a rectangle, then it is a ?
Answer: Parallelogram. Rectangles are special parallelograms with right angles, maintaining opposite sides parallel and equal.
Flashcard 20: Which option is always true: If a quadrilateral is a square, then it is a ?
Answer: Rectangle and rhombus (and parallelogram). Squares inherit properties of rectangles (right angles, congruent diagonals) and rhombuses (equal sides, perpendicular diagonals), thus also parallelograms.
Flashcard 21: Identify the most specific classification: a rhombus with one right angle.
Answer: Square. One right angle in a rhombus makes all angles right because opposite angles are equal and consecutive ones supplementary.
Flashcard 22: Identify the most specific classification: a rectangle with all sides congruent.
Answer: Square. A rectangle with all sides congruent becomes a square, combining equal sides and right angles for maximum symmetry.
Flashcard 23: Identify the most specific classification: a parallelogram with all sides congruent.
Answer: Rhombus. All congruent sides in a parallelogram classify it as a rhombus, inheriting perpendicular bisecting diagonals.
Flashcard 24: Identify the most specific classification: a parallelogram with one right angle.
Answer: Rectangle. One right angle in a parallelogram forces all angles to be right due to opposite angles being equal and consecutive ones supplementary.