Geometry
Legal Reasons
Level 7
Triangle Congruence
Theorems, Properties of Parallelograms How
to Play | Game
Levels | Reasons | Cards
| Game Board | Writing
Proofs
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1
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Two Angles of a Triangle Theorem
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If two angles in one triangle
are congruent to two angles in another triangle, then the third
angles are congruent.
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2
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SSS Congruence Theorem
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If, in two triangles, three sides of one
are congruent to three sides of the other, then the triangles are
congruent.
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3
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SAS Congruence Theorem
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If, in two triangles, two sides and the included
angle of one are congruent to two sides and the included
angle of the other, then the triangles are congruent.
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4
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ASA Congruence Theorem
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If, in two triangles, two angles and the
included side of one are congruent to two angles and the
included side of the other, then the two triangles are congruent.
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5
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AAS Congruence Theorem
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If, in two triangles, two angles
and a non-included
side of one are congruent respectively
to two angles and the corresponding
non-included side
of the other, then the triangles are congruent.
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6
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Properties of a Parallelogram Theorem
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In any parallelogram:
- opposite sides are congruent;
- opposite angles are congruent;
- the diagonals intersect at their midpoints.
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7
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Parallel Line Theorem
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The distance between two given parallel lines
is constant.
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8
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Parallelogram Symmetry Theorem
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Every parallelogram has 2-fold rotation symmetry
about the intersection of its diagonals.
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9
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Sufficient Conditions for a Parallelogram
Theorem
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If, in a quadrilateral,
- both pairs of opposite sides are congruent,
or
- both pairs of opposite angles are congruent,
or
- the diagonals bisect each other, or
- one pair of sides is both parallel and
congruent,
then the quadrilateral is a parallelogram.
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