Geometry Chapters 4/5

Front 1

Corresponding Angles Postulate

Back 1

Suppose two coplanar lines are cut by a transversal.

a. If two corresponding angles have the same measure, then the lines are parallel.

b. If the lines are parallel, then corresponding angles have the same measure.

(// Lines => Corres. Angles Congruent, Corres. Angles Congruent => // Lines)

Front 2

Corresponding Parts of Congruent Figures (CPCF) Theorem

Back 2

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

Front 3

A-B-C-D Theorem

Back 3

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

Front 4

Reflexive Property of Congruence (and Equality)

Back 4

For any figures F, G, and H:

F = F / F ≅ F

Front 5

Symmetric Property of Congruence (and Equality)

Back 5

For any figures F, G, and H:

If F = G, then G = F. / If F ≅ G, then G ≅ F.

Front 6

Transitive Property of Congruence (and Equality)

Back 6

For any figures F, G, and H:

If F = G and G = H, then F = H. / If F ≅ G and G ≅ H, then F ≅ H.

Front 7

Segment Congruence Theorem

Back 7

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

Front 8

Angle Congruence Theorem

Back 8

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

Front 9

Perpendicular Bisector

Back 9

In a plane, the line containing the midpoint of the segment and perpendicular to the segment. In space, the plane that is perpendicular to the segment and contains the midpoint of the segment.

Front 10

Circle

Back 10

The set of points in a plane at a certain distance (its radius) from a certain point (its center)

Front 11

Midpoint

Back 11

The point on the segment equidistant from the segment's endpoints.

Front 12

Congruence

Back 12

Two figures G and F are congruent figures (written F ≅ G) if and only if G is the image of F under an isometry.

Front 13

Angle Bisector

Back 13

The ray with points in the interior of an angle that forms two angles of equal measure with the sides of the angle.

Front 14

Reflection

Back 14

A transformation in which each point is mapped onto its reflection image over a line or plane.

Front 15

Vertical Angles Theorem

Back 15

If two angles are vertical angles, then they have equal measures.

Front 16

// Lines => AIA Congruent Theorem

Back 16

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

Front 17

AIA Congruent => // Lines Theorem

Back 17

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

Front 18

Perpendicular Bisector Theorem

Back 18

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

Front 19

Figure Reflection Theorem

Back 19

If a figure is determined by certain points, then its reflection image is the corresponding figure determined by the reflection images of those points.

Front 20

auxiliary figure

Back 20

A figure that is added to a given figure, often to aid in completing proofs.

Front 21

Uniqueness of Parallels Theorem (Playfair’s Parallel Postulate)

Back 21

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

Front 22

Triangle-Sum Theorem

Back 22

The sum of the measures of the angles of a triangle is 180.

Front 23

Quadrilateral-Sum Theorem

Back 23

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

Front 24

Polygon-Sum Theorem

Back 24

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