C972 College Geometry
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Free C972 College Geometry Questions
What is the sum of interior angles of a convex heptagon?
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(7-2)180° = 900°
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7180°
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5*180°
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1260°
Explanation
The sum of interior angles of a polygon with n sides is given by the formula (n-2) * 180°. For a heptagon, n = 7, so the sum is (7 - 2) * 180° = 900°. This formula works for any convex polygon by dividing it into triangles from a single vertex.
Which is true for similar triangles?
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Corresponding angles equal, sides proportional
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All angles equal, sides equal
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One pair sides equal
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Diagonals equal
Explanation
Similar triangles are defined by having corresponding angles that are equal and corresponding sides that are proportional. This means the triangles have the same shape but may differ in size. Unlike congruent triangles, which have all sides equal in addition to equal angles, similar triangles maintain only the proportional relationship in their sides while preserving identical angle measures.
Equation of line through (1,2) and (3,8)?
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y - 2 = 3(x - 1)
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Slope = (8-2)/(3-1) = 3
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y = 3x -1
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All of A, B, C
Explanation
To find the equation of a line through two points, first calculate the slope: m = (8 - 2)/(3 - 1) = 6/2 = 3. Using point-slope form with point (1,2): y - 2 = 3(x - 1). Simplifying gives the slope-intercept form: y = 3x - 1. All three statements describe correct steps or forms of the line equation.
In a lesson on non-Euclidean geometry, students watch a video on spherical surfaces. What changes on a globe compared to flat paper?
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Parallel lines may intersect
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Triangles have exactly 180°
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Distances are preserved
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Rectangles exist
Explanation
On a spherical surface, the parallel postulate of Euclidean geometry does not hold. Lines of longitude, for example, are considered “lines” on the sphere and they converge at the poles, meaning that lines that start parallel can intersect. This is a key feature of spherical geometry, which contrasts with the flat-plane behavior students are familiar with.
What does it mean for points to be collinear?
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Points on the same line
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Points on different planes
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Points that intersect
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Points in the middle of a segment
Explanation
To say that points are collinear means that all of the points lie on a single straight line. This term is used in geometry to describe the alignment of points and helps determine relationships among segments, rays, and planes. Collinear points share the same path, and their positions can be connected by one straight line without any deviation. The other options describe different geometric relationships that do not reflect the definition of collinearity.
What is the definition of coplanar points?
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Points on the same line
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Points on the same plane
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Points that intersect
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Points on different planes
Explanation
Coplanar points are points that lie on the same plane. A plane is a flat surface that extends indefinitely, and any group of points that can be placed together on such a surface are considered coplanar. This concept applies even if the points do not lie in a straight line or intersect; they simply need to share the same plane. Coplanarity is broader than collinearity, since many different arrangements of points can lie in a single plane.
Which is not a property of a kite?
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Two pairs adjacent equal sides
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Diagonals perpendicular
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One diagonal bisected
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Opposite angles equal
Explanation
A kite has two pairs of adjacent sides that are equal, and its diagonals are perpendicular with one diagonal bisected. However, unlike parallelograms or rhombuses, opposite angles in a kite are not generally equal. Only the angles between unequal sides may be equal, so "opposite angles equal" is not a universal property of kites.
To teach reflection symmetry, a teacher folds a figure. What must coincide?
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Corresponding points
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Line of reflection is perpendicular bisector
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Angles preserved
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All of the above
Explanation
Reflection symmetry occurs when a figure can be folded along a line so that one half maps exactly onto the other. For this to happen, corresponding points must coincide, the line of reflection must act as the perpendicular bisector of segments joining corresponding points, and angles must be preserved to maintain congruence. Therefore, all these conditions are required to demonstrate reflection symmetry
What is the line about which Triangle DEF is reflected in B2?
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y=0
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y=1
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x=0
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y=x
Explanation
In a reflection, a figure is flipped across a line called the line of reflection. Each point of the figure is mirrored over this line, creating a congruent image on the opposite side. For Triangle DEF in B2, the line y=0, which is the x-axis, serves as the line of reflection. This means that each point of the triangle is mirrored across the x-axis, maintaining the triangle’s shape and size but changing its orientation relative to the axis.
What is a plane?
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A straight path with a defined endpoint
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A location with size
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A curved surface with thickness
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A flat surface that extends without end and has no thickness
Explanation
A plane in geometry is understood as an infinite flat surface with no thickness. It extends endlessly in all directions and has length and width but no depth. This concept is foundational in geometry because many shapes, lines, and angles are defined within or relative to a plane. The other options describe different geometric ideas, but only one matches the precise definition of a plane.
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