Describe Cross-Sections of 3D Figures - 7th Grade Math
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Which statement is true for a pyramid slice parallel to the base: congruent or similar to the base?
Which statement is true for a pyramid slice parallel to the base: congruent or similar to the base?
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Similar to the base. Pyramids taper, so parallel cuts create smaller similar shapes.
Similar to the base. Pyramids taper, so parallel cuts create smaller similar shapes.
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Identify the cross section: a right rectangular prism is cut by a plane parallel to the base.
Identify the cross section: a right rectangular prism is cut by a plane parallel to the base.
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Rectangle. Parallel cuts to prism bases preserve the base shape.
Rectangle. Parallel cuts to prism bases preserve the base shape.
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Identify the cross section: a cube is cut by a plane parallel to a face.
Identify the cross section: a cube is cut by a plane parallel to a face.
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Square. Cube faces are squares; parallel cuts preserve this shape.
Square. Cube faces are squares; parallel cuts preserve this shape.
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Identify the cross section: a right rectangular pyramid is cut by a plane parallel to the base.
Identify the cross section: a right rectangular pyramid is cut by a plane parallel to the base.
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Rectangle. Pyramid slices parallel to base are similar rectangles.
Rectangle. Pyramid slices parallel to base are similar rectangles.
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Identify the cross section: a right rectangular pyramid is cut by a plane through the apex and perpendicular to the base.
Identify the cross section: a right rectangular pyramid is cut by a plane through the apex and perpendicular to the base.
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Triangle. Vertical cuts through pyramid apex create triangles.
Triangle. Vertical cuts through pyramid apex create triangles.
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Identify the cross section: a right rectangular pyramid is cut by a plane perpendicular to the base and not through the apex.
Identify the cross section: a right rectangular pyramid is cut by a plane perpendicular to the base and not through the apex.
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Trapezoid. Perpendicular cuts missing the apex form trapezoids.
Trapezoid. Perpendicular cuts missing the apex form trapezoids.
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Which $2$D figure is impossible from slicing a right rectangular prism: circle, rectangle, or parallelogram?
Which $2$D figure is impossible from slicing a right rectangular prism: circle, rectangle, or parallelogram?
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Circle. Prisms have straight edges, so no curved cross sections.
Circle. Prisms have straight edges, so no curved cross sections.
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Which $2$D figure is impossible from slicing a right rectangular pyramid: rectangle, trapezoid, or circle?
Which $2$D figure is impossible from slicing a right rectangular pyramid: rectangle, trapezoid, or circle?
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Circle. Pyramids have straight edges, so no curved cross sections.
Circle. Pyramids have straight edges, so no curved cross sections.
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What $2$D figure results when a right rectangular pyramid is sliced by a plane that cuts all $4$ lateral faces?
What $2$D figure results when a right rectangular pyramid is sliced by a plane that cuts all $4$ lateral faces?
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A quadrilateral. Cutting all 4 lateral faces creates a 4-sided figure.
A quadrilateral. Cutting all 4 lateral faces creates a 4-sided figure.
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Which statement is true for a prism slice parallel to the base: congruent or similar to the base?
Which statement is true for a prism slice parallel to the base: congruent or similar to the base?
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Congruent to the base. Prisms have uniform cross sections, so cuts are congruent.
Congruent to the base. Prisms have uniform cross sections, so cuts are congruent.
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What is the name of the $2$D figure formed by the intersection of a plane and a solid?
What is the name of the $2$D figure formed by the intersection of a plane and a solid?
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A cross section (a plane section). The intersection of a plane with a 3D solid creates a 2D shape.
A cross section (a plane section). The intersection of a plane with a 3D solid creates a 2D shape.
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What $2$D figure results when a right rectangular prism is sliced parallel to its base?
What $2$D figure results when a right rectangular prism is sliced parallel to its base?
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A rectangle congruent to the base. Parallel cuts preserve shape and size of the base.
A rectangle congruent to the base. Parallel cuts preserve shape and size of the base.
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What $2$D figure results when a right rectangular pyramid is sliced parallel to its base?
What $2$D figure results when a right rectangular pyramid is sliced parallel to its base?
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A rectangle similar to the base. Parallel cuts to pyramid bases create similar, not congruent shapes.
A rectangle similar to the base. Parallel cuts to pyramid bases create similar, not congruent shapes.
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What $2$D figure results when a right rectangular prism is sliced perpendicular to its base?
What $2$D figure results when a right rectangular prism is sliced perpendicular to its base?
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A rectangle. Perpendicular cuts through a prism create rectangles.
A rectangle. Perpendicular cuts through a prism create rectangles.
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Which $2$D figure can result when a right rectangular prism is sliced by a slanted plane not parallel to any face?
Which $2$D figure can result when a right rectangular prism is sliced by a slanted plane not parallel to any face?
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A parallelogram. Slanted cuts through opposite edges create parallelograms.
A parallelogram. Slanted cuts through opposite edges create parallelograms.
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What $2$D figure results when a right rectangular pyramid is sliced perpendicular to its base through the apex?
What $2$D figure results when a right rectangular pyramid is sliced perpendicular to its base through the apex?
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A triangle. Cuts through the apex create triangular cross sections.
A triangle. Cuts through the apex create triangular cross sections.
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What $2$D figure results when a right rectangular pyramid is sliced perpendicular to its base but not through the apex?
What $2$D figure results when a right rectangular pyramid is sliced perpendicular to its base but not through the apex?
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A trapezoid. Perpendicular cuts not through apex create 4-sided figures.
A trapezoid. Perpendicular cuts not through apex create 4-sided figures.
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Identify the cross section of a cube sliced through the center, perpendicular to the base.
Identify the cross section of a cube sliced through the center, perpendicular to the base.
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A rectangle. Perpendicular cuts through a cube create rectangles.
A rectangle. Perpendicular cuts through a cube create rectangles.
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Identify the cross section of a cube sliced parallel to one face.
Identify the cross section of a cube sliced parallel to one face.
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A square. A cube's faces are squares, so parallel cuts yield squares.
A square. A cube's faces are squares, so parallel cuts yield squares.
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What $2$D figure results when a right rectangular prism is sliced parallel to one lateral face?
What $2$D figure results when a right rectangular prism is sliced parallel to one lateral face?
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A rectangle congruent to that face. Parallel cuts to any face preserve that face's shape and size.
A rectangle congruent to that face. Parallel cuts to any face preserve that face's shape and size.
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Identify the cross-section of a right rectangular prism cut perpendicular to its base.
Identify the cross-section of a right rectangular prism cut perpendicular to its base.
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A rectangle. Any perpendicular cut through a prism creates a rectangle.
A rectangle. Any perpendicular cut through a prism creates a rectangle.
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Identify the cross-section of a right rectangular pyramid cut parallel to its base.
Identify the cross-section of a right rectangular pyramid cut parallel to its base.
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A rectangle (similar to the base). Parallel cuts create proportionally smaller rectangles.
A rectangle (similar to the base). Parallel cuts create proportionally smaller rectangles.
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Identify the cross-section of a right rectangular pyramid cut through the apex and perpendicular to the base.
Identify the cross-section of a right rectangular pyramid cut through the apex and perpendicular to the base.
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A triangle. Vertical cuts through the apex create triangular sections.
A triangle. Vertical cuts through the apex create triangular sections.
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Which $2$D shape results from a right rectangular pyramid sliced by a plane that cuts the base but misses the apex?
Which $2$D shape results from a right rectangular pyramid sliced by a plane that cuts the base but misses the apex?
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A trapezoid. Missing the apex creates parallel sides (trapezoid).
A trapezoid. Missing the apex creates parallel sides (trapezoid).
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Which $2$D shape results from a right rectangular pyramid sliced by a plane that intersects $3$ lateral faces but not the base?
Which $2$D shape results from a right rectangular pyramid sliced by a plane that intersects $3$ lateral faces but not the base?
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A triangle. Three lateral faces meet at three edges, forming a triangle.
A triangle. Three lateral faces meet at three edges, forming a triangle.
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