Geometry Legal Reasons
Level 7
Triangle Congruence Theorems, Properties of Parallelograms
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1

Two Angles of a Triangle Theorem

If two angles in one triangle are congruent to two angles in another triangle, then the third angles are congruent.

2

SSS Congruence Theorem

If, in two triangles, three sides of one are congruent to three sides of the other, then the triangles are congruent.

3

SAS Congruence Theorem

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.

4

ASA Congruence Theorem

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.

5

AAS Congruence Theorem

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.

6

Properties of a Parallelogram Theorem

In any parallelogram:

1. opposite sides are congruent;
2. opposite angles are congruent;
3. the diagonals intersect at their midpoints.

7

Parallel Line Theorem

The distance between two given parallel lines is constant.

8

Parallelogram Symmetry Theorem

Every parallelogram has 2-fold rotation symmetry about the intersection of its diagonals.

9

Sufficient Conditions for a Parallelogram Theorem

If, in a quadrilateral,

1. both pairs of opposite sides are congruent, or
2. both pairs of opposite angles are congruent, or
3. the diagonals bisect each other, or
4. one pair of sides is both parallel and congruent,

then the quadrilateral is a parallelogram.

Nguồn: http://www.themathlab.com/geometry/mathcourt/level7/reasonslevel7.htm