Chapter 8 Notecards
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Diagonal | diagonal of a polygon is a segment that joins two nonconsecutive vertices
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| Polygon Interior Angles Theorem | The sum of the measures of the interior angles of a convex n-gon is (n-2)180
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| Interior Angles of a Quadrilateral Corollary | The sum of the measures of the interior angles of a quadrilateral is 360
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| Polygon Exterior Angles Theorem | The sum of the measures of the exterior angles of a convex polygon, one angle at each vertex, is 360.
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| Parallelogram | a quadrilateral with both pairs of opposite sides parallel.
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| Theorem 8.3 | if a quadrilateral is a parallelogram then its opposite sides are congruent
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| Theorem 8.4 | if a quadrilateral is a parallelogram then its opposite angles are congruent
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| Theorem 8.5 | if a quadrilateral is a parallelogram then its consecutive angles are supplementary
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| Theorem 8.6 | if a quadrilateral is a parallelogram then its diagonals bisect each other
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| Theorem 8.7 | if both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram
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| Theorem 8.8 | if both pairs of opposite angles of a quadrilateral are congruent then the quadrilateral is a parallelogram
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| Theorem 8.9 | if one pair of opposite sides of a quadrilateral are congruent and parallel then the quadrilateral is a parallelogram
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| Theorem 8.10 | if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram
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| Rhombus | a parallelogram with four congruent sides
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| Rectangle | a parallelogram with four right angles
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| Square | a parallelogram with four congruent sides and four right angles.
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| Rhombus Corollary | a quadrilateral is a rhombus if and only if it has four congruent sides
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| Rectangle Corollary | a quadrilateral is a rectangle if and only if it has four right angles
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| Square Corollary | a quadrilateral is a square if and only if it is a rhombus and a rectangle
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| Theorem 8.11 | a parallelogram is a rhombus if and only if its diagonals are perpendicular
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| Theorem 8.12 | a parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles
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| Theorem 8.13 | a parallelogram is a rectangle if and only if its diagonals are congruent
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| Trapezoid | a quadrilateral with exactly one pair of parallel sides
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| Bases of a Trapezoid | The parallel sides are the bases and there is only two pairs of base angles.
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| Legs of a Trapezoid | the nonparallel sides
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| Theorem 8.14 | if a trapezoid is isosceles then each pair of base angles is congruent
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| Theorem 8.15 | if a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid
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| Theorem 8.16 | a trapezoid is isosceles if and only if its diagonals are congruent
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| Midsegment of a Trapezoid | the segment that connects the midpoints of its legs
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| Midsegment Theorem for Trapezoids | the midsegment of a trapezoid is parallel to each base and its length is one half the sum of the lengths of the bases
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| Kite | a quadrilateral that has two pairs of consecutive congruent sides, but opposite sides are not congruent
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| Theorem 8.18 | if a quadrilateral is a kite then its diagonals are perpendicular
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| Theorem 8.19 | if a quadrilateral is a kite then exactly one pair of opposite angles are congruent
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