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23 Cards in this Set
- Front
- Back
Polygon Angle- Sum Theorem (Theorem 6-1)
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The sum of the measure of the interior angles of an n-gon is (n-2)180
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Corollary to the Polygon Angle-Sum Theorem
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The measure of each interior angle of a regular n-gon is [(n-2)180]/n
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Polygon Exterior Angle-Sum Theorem (Theorem 6-2)
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The sum of the measures of the exterior angles of a polygon, one at each vertex is 360.
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Theorem 6-3
If a quadrilateral is a parallelogram, then its what are congruent? |
opposite sides
If a quadrilateral is a parallelogram, then its opposite sides are congruent. |
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Theorem 6-4
If a quadrilateral is a parallelogram, then its what are supplementary? |
consecutive angles
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary. |
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Theorem 6-5
If a quadrilateral is a parallelogram, then its what are congruent? |
opposite sides
If a quadrilateral is a parallelogram, then its opposite sides are congruent. |
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Theorem 6-6
If a quadrilateral is a parallelogram, then its what bisect each other? |
diagonals
If a quadrilateral is a parallelogram, then its diagonals bisect each other. |
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Theorem 6-7
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off what on every transversal? |
congruent segments
If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. |
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Theorem 6-8
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a what? |
parallelogram
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
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Theorem 6-9
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a what?. |
parallelogram
If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram. |
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Theorem 6-10
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a what? |
parallelogram
If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. |
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Theorem 6-11
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a what? |
parallelogram
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. |
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Theorem 6-12
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a what? |
parallelogram
If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram |
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Theorem 6-13
If a parallelogram is a rhombus, then its diagonals are what? |
perpendicular
If a parallelogram is a rhombus, then its diagonals are perpendicular. |
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Theorem 6-14
If a parallelogram is a rhombus, then each diagonal bisects what? |
a pair of opposite angles
If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles. |
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Theorem 6-15
If a parallelogram is a rectangle, then its diagonals are what? |
congruent
If a parallelogram is a rectangle, then its diagonals are congruent. |
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Theorem 6-16
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a what? |
rhombus
If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus. |
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Theorem 6-17
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a what?. |
rhombus
If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus. |
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Theorem 6-18
If the diagonals of a parallelogram are congruent, then the parallelogram is a what? |
rectangle
If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. |
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Theorem 6-19
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is what? |
congruent
If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. |
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Theorem 6-20
If a quadrilateral is an isosceles trapezoid, then its diagonals are what? |
congruent
If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent. |
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Theorem 6-21
If a quadrilateral is a trapezoid then what two conditions are met? |
1) the mid-segment is parallel to the bases
2) the length of the mid-segment is half the sum of the length of the bases. |
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Theorem 6-22
If a quadrilateral is a kite, then its diagonals are what? |
perpendicular
If a quadrilateral is a kite, then its diagonals are perpendicular. |