Geometry Legal Reasons Level 5

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1

Corresponding Parts of Congruent Figures (CPCF) Theorem

If two figures are congruent, then any pair of corresponding parts is congruent.

2

A-B-C-D Theorem

Every isometry preserves Angle Measure, Betweenness, Collinearity (lines), and Distance (lengths of segments).

3

Theorem (Equivalence Properties of @ )

F@ F (Reflexive Property of @ )
If F@ G, then G@ F.
(Symmetric Property of @ )
If F@ G and G@ H, then F@ H
(Transitive Property of @ )

4

Segment Congruence Theorem

Two segments are congruent if and only if they have the same length.

5

Angle Congruence Theorem

Two angles are congruent if and only if they have the same measure.

6

// Lines Þ AIA @ Theorem

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

7

AIA @ Þ // Lines Theorem

If two lines are cut by a transversal and form congruent alternate interior angles, then the lines are parallel.

8

AEA @ Þ // Lines Theorem

If two lines are cut by a transversal and form congruent alternate exterior angles, then the lines are parallel.

10

Perpendicular Bisector Theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

11

Uniqueness of Parallels Theorem (Playfair's Parallel Postulate)

Through a point not on a line, there is exactly one line parallel to the given line.

12

Triangle-Sum Theorem

The sum of the measures of the angles of a triangle in 180° .

13

Quadrilateral-Sum Theorem

The sum of the measures of the angles of a convex quadrilateral is 360° .

14

Polygon-Sum Theorem

The sum of the measures of the angles of a convex n-gon is (n-2)180° .