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15 Cards in this Set
- Front
- Back
A great circle of a sphere is...
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a set of points that is the intersection of the sphere and a plane containing the center of the sphere.
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Antipodal points...
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are the two points of intersection of a sphere with a line through its center.
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A birectangular quadrilateral...
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is a quadrilateral that has two sides perpendicular to a third side.
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Parts of a birectangular quadrilateral.
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Angle A and angle B are base angles.
Angle C and angle D are summit angles. |
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A Saccheri quadrilateral...
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is a birectangular quadrilateral whose legs are equal.
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The summit angles of a Saccheri quadrilateral...
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are equal.
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The line segments connecting the midpoints of the base and summit of a Saccheri quadrilateral are...
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perpendicular to them both.
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If the legs of a birectangular quadrilateral are unequal, then...
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the summit angles opposite them are unequal in the same order.
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If the summit angles of a birectangular quadrilateral are unequal, then...
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the legs opposite them are unequal in the same order.
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The Lobachevskian Postulate
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The summit angles of Saccheri quadrilateral are acute.
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Lobachevskian Theorem 1
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The summit of a Saccheri quadrilateral is longer than its base
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Lobechevskian Theorem 2
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A midsegment of a triangle is less than half as long as the third side.
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Lobachevskian Theorem 3
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The sum of the angles of a triangle is less than 180°.
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Corollary to Lobachevskian Theorem 3
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The sum of the angles of a quadrilateral is less than 360°.
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Lobachevskian Theorem 4
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If two triangles are similar, they must also be congruent.
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