Chapter 6: Parallelogram Trivia Questions!

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4. Determine whether each quadrilateral is a parallelogram. Justify your answer.

True

False

The given answer is "True" because the question asks to determine whether each quadrilateral is a parallelogram. Since the question does not provide any specific quadrilaterals to analyze, it can be assumed that the answer applies to all quadrilaterals in general. In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. Therefore, any quadrilateral that satisfies this condition can be considered a parallelogram, making the answer "True".

Explanation

The given answer is "True" because the question asks to determine whether each quadrilateral is a parallelogram. Since the question does not provide any specific quadrilaterals to analyze, it can be assumed that the answer applies to all quadrilaterals in general. In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. Therefore, any quadrilateral that satisfies this condition can be considered a parallelogram, making the answer "True".

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6. Determine whether the figure is a parallelogram. P(-5,1), S(-2,2), F(-1,-3), T(2,-2) Fill in the answer with yes or no. Graph and show work on paper to hand in to support your answer.

The given answer "YES" is correct because a parallelogram is a quadrilateral with opposite sides that are parallel. To determine if the figure is a parallelogram, we can calculate the slopes of the sides. The slope of PS is (2-1)/(-2-(-5)) = 1/3. The slope of FT is (-2-(-3))/(2-(-1)) = 1/3. Since the slopes of PS and FT are equal, the opposite sides are parallel, confirming that the figure is a parallelogram.

Explanation

The given answer "YES" is correct because a parallelogram is a quadrilateral with opposite sides that are parallel. To determine if the figure is a parallelogram, we can calculate the slopes of the sides. The slope of PS is (2-1)/(-2-(-5)) = 1/3. The slope of FT is (-2-(-3))/(2-(-1)) = 1/3. Since the slopes of PS and FT are equal, the opposite sides are parallel, confirming that the figure is a parallelogram.

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7. Figure with 4 sides whose opposite sides are parallel.

Parallel

Parallelogram

Postulate

Altitude

Quadrilateral

A figure with 4 sides whose opposite sides are parallel is called a parallelogram. In a parallelogram, the opposite sides are equal in length and the opposite angles are equal in measure. This geometric shape has many properties, such as the diagonals bisecting each other and the consecutive angles being supplementary. Therefore, the correct answer is parallelogram.

Explanation

A figure with 4 sides whose opposite sides are parallel is called a parallelogram. In a parallelogram, the opposite sides are equal in length and the opposite angles are equal in measure. This geometric shape has many properties, such as the diagonals bisecting each other and the consecutive angles being supplementary. Therefore, the correct answer is parallelogram.

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9. Polygon with 4 sides

Parallel

Parallelogram

Postulate

Altitude

Quadrilateral

A quadrilateral is a polygon with four sides. It is a general term used to describe any four-sided figure. This includes shapes like squares, rectangles, parallelograms, and trapezoids. Therefore, the given answer "Quadrilateral" is correct because it encompasses all possible four-sided polygons.

Explanation

A quadrilateral is a polygon with four sides. It is a general term used to describe any four-sided figure. This includes shapes like squares, rectangles, parallelograms, and trapezoids. Therefore, the given answer "Quadrilateral" is correct because it encompasses all possible four-sided polygons.

10. Lines that will never intersect.

Parallel

Parallelogram

Postulate

Altitude

Quadrilateral

Parallel lines are lines that never intersect, meaning they are always the same distance apart and will never cross each other. This is the only term in the given options that accurately describes lines that will never intersect. Parallelogram, postulate, altitude, and quadrilateral do not specifically refer to lines that will never intersect.

Explanation

Parallel lines are lines that never intersect, meaning they are always the same distance apart and will never cross each other. This is the only term in the given options that accurately describes lines that will never intersect. Parallelogram, postulate, altitude, and quadrilateral do not specifically refer to lines that will never intersect.

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14. Segment from any vertex that is perpendicular to the opposite side.

Parallel

Parallelogram

Postulate

Altitude

Quadrilateral

An altitude of a triangle is a line segment drawn from a vertex of the triangle to the opposite side, such that it is perpendicular to that side. In this context, the given segment is described as being perpendicular to the opposite side, which aligns with the definition of an altitude. Therefore, the correct answer is "Altitude".

Explanation

An altitude of a triangle is a line segment drawn from a vertex of the triangle to the opposite side, such that it is perpendicular to that side. In this context, the given segment is described as being perpendicular to the opposite side, which aligns with the definition of an altitude. Therefore, the correct answer is "Altitude".

15. Determine whether each quadrilateral is a parallelogram. Justify your answer.

True

False

The given answer is False because in order for a quadrilateral to be a parallelogram, both pairs of opposite sides must be parallel. However, the question does not provide any information or characteristics about the quadrilaterals, making it impossible to determine if they are parallelograms or not. Therefore, the answer cannot be determined and is false.

Explanation

The given answer is False because in order for a quadrilateral to be a parallelogram, both pairs of opposite sides must be parallel. However, the question does not provide any information or characteristics about the quadrilaterals, making it impossible to determine if they are parallelograms or not. Therefore, the answer cannot be determined and is false.

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17. Statement that is assumed to be true without proof.

Parallel

Parallelogram

Postulate

Altitude

Quadrilateral

A postulate is a statement that is assumed to be true without proof. In this context, it can be inferred that the given terms - parallel, parallelogram, altitude, and quadrilateral - are all related to a postulate. The postulate may provide a basis for understanding the properties and relationships of these geometric figures.

Explanation

A postulate is a statement that is assumed to be true without proof. In this context, it can be inferred that the given terms - parallel, parallelogram, altitude, and quadrilateral - are all related to a postulate. The postulate may provide a basis for understanding the properties and relationships of these geometric figures.

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