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This quiz will have theorem questions along with sometimes, always,and never questions.
Questions and Answers
1.
If both pairs of opposite sides of a quadrilateral are congruent, the the quadrilateral is a ____________________________
Explanation If both pairs of opposite sides of a quadrilateral are congruent, it means that the lengths of the opposite sides are equal. This is a property of parallelograms, where the opposite sides are parallel and congruent. Therefore, if a quadrilateral has congruent opposite sides, it can be concluded that it is a parallelogram.
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2.
A____________________ is a quadrilateral with exactly one pair of parallel sides.
Explanation A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid, the two non-parallel sides are called legs, while the parallel sides are called bases. The bases can be of different lengths, but the legs are always non-parallel. This definition distinguishes a trapezoid from other quadrilaterals, such as parallelograms or rectangles, which have two pairs of parallel sides. Therefore, a trapezoid is the correct answer for a quadrilateral with exactly one pair of parallel sides.
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3.
A trapeziod with congruent legs is called an ______________________________________
Explanation An isosceles trapezoid is a trapezoid with two congruent legs. The term "isosceles" refers to the fact that two sides of the trapezoid are equal in length. In this case, the congruent legs are the two non-parallel sides of the trapezoid. The other two sides, called the bases, are parallel but not necessarily congruent. Therefore, the correct answer for this question is "Isosceles Trapezoid."
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4.
The _______________________ of a trapezoid is the segment that joins the midpoints of the legs.
Explanation The median of a trapezoid is the segment that joins the midpoints of the legs. The midpoint of a line segment is the point that divides the segment into two equal parts. Therefore, the median of a trapezoid connects the midpoints of the legs, dividing the trapezoid into two equal areas. It is an important line segment in trapezoid geometry.
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5.
Base angles of an isosceles trapezoid are __________________________________.
Explanation The base angles of an isosceles trapezoid are congruent. This means that the two angles formed by the non-parallel sides and one of the parallel sides are equal in measure. In an isosceles trapezoid, the non-parallel sides are equal in length, so it follows that the angles opposite these sides are also equal. Therefore, the base angles of an isosceles trapezoid are congruent.
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6.
The median of a trapezoid is _____________________________ to the bases.
Explanation The median of a trapezoid is parallel to the bases because it divides the trapezoid into two congruent triangles. Since the bases of a trapezoid are parallel, the median, which connects the midpoints of the non-parallel sides, must also be parallel to the bases. This can be proven using the properties of parallel lines and congruent triangles.
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7.
The median of a trapezoid has a length of half the sum of the ___________________________________________________________.
Explanation The median of a trapezoid has a length of half the sum of the base lengths. This is because the median of a trapezoid is a line segment that connects the midpoints of the two non-parallel sides. Since the midpoints divide the bases into two equal parts, the length of the median is half the sum of the base lengths.
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8.
A quadrilateral with exactly two distinct pairs of adjacent congruent sides is a_________________________________________________.
Explanation A quadrilateral with exactly two distinct pairs of adjacent congruent sides is a kite. A kite is a quadrilateral that has two pairs of congruent adjacent sides, with one pair of opposite angles congruent. This shape resembles the shape of a kite, with two longer sides and two shorter sides. Therefore, the given answer, "kite," is correct.
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9.
If two lines are parallel, then all points on one line are _____________________________________ from the other line.
Explanation If two lines are parallel, it means that they will never intersect. Therefore, all points on one line will always be the same distance away from the other line. This distance is called the distance of equidistance, meaning that all points on one line are equidistant from the other line.
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10.
A line that contains the midpoint of one side of a triangle and is parallel to another side passes through the _________________________ of the third side.
Explanation When a line passes through the midpoint of one side of a triangle and is parallel to another side, it is called a midline. The midline divides the triangle into two smaller triangles of equal area. The midpoint of the third side is the point where the midline intersects the third side. This is because the midline is parallel to the third side, so it will intersect it at its midpoint. Therefore, the correct answer is "Midpoint".
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11.
If three parallel lines cut off congruent segments on one transversal, then they cut off ________________________________________ segments on every transversal.
Explanation If three parallel lines cut off congruent segments on one transversal, it means that the segments formed by the intersection of the parallel lines and the transversal are equal in length. This is because parallel lines create corresponding angles that are congruent, which in turn create congruent triangles. Therefore, if the segments are congruent on one transversal, they will also be congruent on every other transversal intersecting the same parallel lines.
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12.
Opposite sides are parallel.
A.
All:Parallelogram, Rectangle, Rhombus, Square
B.
Rectangle
C.
Rhombus
D.
Square
E.
Parallelogram
Correct Answer A. All:Parallelogram, Rectangle, Rhombus, Square
Explanation The given statement "Opposite sides are parallel" is true for all the shapes listed: parallelogram, rectangle, rhombus, and square. In a parallelogram, opposite sides are always parallel. A rectangle is a special type of parallelogram where all angles are right angles, and therefore opposite sides are also parallel. A rhombus is a special type of parallelogram where all sides are equal in length, and therefore opposite sides are parallel. A square is a special type of rectangle and rhombus, where all angles are right angles and all sides are equal in length, making opposite sides parallel as well.
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13.
Opposite sides are congruent.
A.
All:Parallelogram, Rectangle, Rhombus, Square
B.
Rectangle
C.
Square
D.
Rhombus
E.
Parallelogram
Correct Answer A. All:Parallelogram, Rectangle, Rhombus, Square
Explanation All of the shapes listed (parallelogram, rectangle, rhombus, square) have opposite sides that are congruent. In a parallelogram, opposite sides are parallel and congruent. A rectangle is a special type of parallelogram with all right angles, so its opposite sides are also congruent. A rhombus is a parallelogram with all sides congruent, so its opposite sides are also congruent. A square is a special type of rhombus with all right angles, so its opposite sides are congruent as well. Therefore, the statement "opposite sides are congruent" applies to all of the shapes listed.
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14.
All sides are congruent.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Parallelogram, Square
C.
Rhombus, Square
D.
Rectangle, Rhombus
E.
Rectangle, Parallelogram
Correct Answer C. Rhombus, Square
Explanation The statement "All sides are congruent" means that all sides of the shape are equal in length. A rhombus and a square both have this property, as all four sides of these shapes are equal. Therefore, the answer is rhombus and square. A parallelogram and a rectangle do not necessarily have all sides congruent, so they are not the correct answer.
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15.
All angles are right angles.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Rhombus, Square
C.
Rectangle, Parallelogram
D.
Rhombus, Rectangle
E.
Rectangle, Square
Correct Answer E. Rectangle, Square
Explanation The correct answer is Rectangle, Square. Both rectangles and squares have all right angles. A rectangle is a quadrilateral with opposite sides equal and all angles equal to 90 degrees. A square is a special type of rectangle where all sides are equal in length. Therefore, both rectangles and squares have all right angles.
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16.
Opposite angles are congruent.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Square
C.
Parallelogram
D.
Rectangle
E.
Rhombus
Correct Answer A. All: Parallelogram, Rectangle, Rhombus, Square
Explanation The given answer states that all parallelograms, rectangles, rhombuses, and squares have congruent opposite angles. This means that in any of these shapes, the angles that are opposite to each other will have the same measure. This property is true for all four types of quadrilaterals mentioned in the answer.
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17.
A diagonal bisects two angles.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Rhombus, Rectangle
C.
Square, Rhombus
D.
Parallelogram, Square
E.
Parallelogram, Rectangle
Correct Answer C. Square, Rhombus
Explanation A diagonal bisects two angles in both a Square and a Rhombus. In a Square, the diagonal bisects the right angles, dividing them into two equal angles of 45 degrees each. In a Rhombus, the diagonal bisects the acute angles, dividing them into two equal angles. Therefore, the correct answer is Square, Rhombus.
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18.
Diagonals are perpendicular.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Rectangle, Square
C.
Rhombus, Rectangle
D.
Square, Rhombus
E.
Parallelogram, Square
Correct Answer D. Square, Rhombus
Explanation The given answer is "Square, Rhombus". This means that both a square and a rhombus have perpendicular diagonals. A square is a special type of rhombus where all sides are equal in length and all angles are right angles. Therefore, since a square is a rhombus, it also has perpendicular diagonals.
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19.
A diagonal forms two congruent triangles.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Parallelogram, Square, Rectangle
C.
Square, Rectangle, Rhombus
D.
Rectangle, Rhombus, Parallelogram
E.
Square, Rhombus, Parallelogram
Correct Answer A. All: Parallelogram, Rectangle, Rhombus, Square
Explanation The statement "A diagonal forms two congruent triangles" is true for all parallelograms, rectangles, rhombuses, and squares. In each of these shapes, drawing a diagonal will divide the shape into two congruent triangles. Therefore, all the options listed (Parallelogram, Rectangle, Rhombus, Square) are correct.
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20.
Diagonals are congruent.
A.
Rectangle, Rhombus
B.
Rhombus, Parallelogram
C.
Parallelogram, Square
D.
Square, Rectangle
Correct Answer D. Square, Rectangle
Explanation The statement "Diagonals are congruent" is a property that is true for both squares and rectangles. In a square, all four sides are equal in length and all angles are right angles, so the diagonals are congruent. In a rectangle, opposite sides are equal in length and all angles are right angles, so the diagonals are also congruent. Therefore, both squares and rectangles satisfy the given statement.
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21.
Diagonals, bisect each other.
A.
All: Parallelogram, Rectangle, Rhombus, Square
B.
Rectangle, Rhombus, Square
C.
Square, Parallelogram, Rhombus
D.
Parallelogram, Rectangle, Square
E.
Rectangle, Rhombus, Parallelogram
Correct Answer A. All: Parallelogram, Rectangle, Rhombus, Square
Explanation In geometry, the diagonals of a parallelogram, rectangle, rhombus, and square bisect each other. This means that the diagonals divide each other into two equal parts. Therefore, all of these shapes have diagonals that bisect each other.
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