geometry

Perpendicular Bisector

A line that forms 90 degree angles and cuts a segment in half. Any point on the perpendicular bisector is equidistant to the endpoints of the segment.

Angle Bisector

A ray or line that cuts an angle in half. Any point on the angle bisector is equidistant to the sides of the angle.

Line of Symmetry

A line that divides a figure into two equal reflections of each other. If you fold the figure over this line, it will lie exactly on top of itself.

Corresponding parts of congruent triangles are congruent (CPCTC)

A theorem stating that if two triangles are congruent, then so are all corresponding parts.

Congruent Sides

Sides that have the exact same length.

Vertex of an Angle

The vertex is where the two rays that form the angle meet.

Corresponding Sides

Two sides that are situated the same way in different objects (in red).

Corresponding Angles

Two angles that are situated the same way in different objects (e.g., angles E and G)

Third Angle Theorem

If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent

Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

Converse of the Isosceles Triangle Theorem

If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent.

Congruent

When two parts of a geometric figure have the same shape and size.

Corresponding

Basic geometric figures that are in the same position in different shapes.

Included side

A side that is between two angles in a triangle

In the figure, LM is the included side between angle L and angle M.

Included angle

An angle that is between two sides in a triangle

In the figure, angle N is the included angle between LN and MN.

Angle-Angle-Angle (AAA)

AAA does NOT prove triangles congruent; DOES show that triangles are SIMILAR.

Side-Side-Angle (SSA)

SSA does NOT prove triangles congruent - do not use!!

Congruent Triangles

3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.

Equiangular Triangle

A triangle whose angles are all congruent.

Scalene Triangle

A triangle that has no congruent sides.

Isosceles Triangle

A triangle with at least two congruent sides.

Equilateral Triangle

A triangle that has all three sides congruent.

Triangle Sum Theorem

The sum of the measures in a triangle is 180 degrees.

Exterior Angle Theorem

The sum of the remote interior angles is equal to the measure of the exterior angle.

Reflexive property

A shape is congruent (equal) to itself. Shapes can be used in more than one figure. Segment RS is used in the red and blue triangles.

Triangle rigidity

If the side lengths of a triangle are given, the triangle can only have one shape.

congruent shapes

two figures that have corresponding congruent sides and angle measures (same exact size and shape)

Perpendicular Bisector

A line that forms 90 degree angles and cuts a segment in half. Any point on the perpendicular bisector is equidistant to the endpoints of the segment.

Angle Bisector

A ray or line that cuts an angle in half. Any point on the angle bisector is equidistant to the sides of the angle.

Line of Symmetry

A line that divides a figure into two equal reflections of each other. If you fold the figure over this line, it will lie exactly on top of itself.

Corresponding parts of congruent triangles are congruent (CPCTC)

A theorem stating that if two triangles are congruent, then so are all corresponding parts.

Congruent Sides

Sides that have the exact same length.

Vertex of an Angle

The vertex is where the two rays that form the angle meet.

Corresponding Sides

Two sides that are situated the same way in different objects (in red).

Corresponding Angles

Two angles that are situated the same way in different objects (e.g., angles E and G)

Third Angle Theorem

If the 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent

Isosceles Triangle Theorem

If 2 sides of a triangle are congruent, then the angles opposite those sides are congruent

Converse of the Isosceles Triangle Theorem

If 2 angles of a triangle are congruent, then the sides opposite of the angles are congruent.

Congruent

When two parts of a geometric figure have the same shape and size.

Corresponding

Basic geometric figures that are in the same position in different shapes.

Included side

A side that is between two angles in a triangle

In the figure, LM is the included side between angle L and angle M.

Included angle

An angle that is between two sides in a triangle

In the figure, angle N is the included angle between LN and MN.

Angle-Angle-Angle (AAA)

AAA does NOT prove triangles congruent; DOES show that triangles are SIMILAR.

Side-Side-Angle (SSA)

SSA does NOT prove triangles congruent - do not use!!

Congruent Triangles

3 pairs of corresponding angles are congruent and 3 pairs of corresponding sides are congruent.

Equiangular Triangle

A triangle whose angles are all congruent.

Scalene Triangle

A triangle that has no congruent sides.

Isosceles Triangle

A triangle with at least two congruent sides.

Equilateral Triangle

A triangle that has all three sides congruent.

Triangle Sum Theorem

The sum of the measures in a triangle is 180 degrees.

Exterior Angle Theorem

The sum of the remote interior angles is equal to the measure of the exterior angle.

Reflexive property

A shape is congruent (equal) to itself. Shapes can be used in more than one figure. Segment RS is used in the red and blue triangles.

Triangle rigidity

If the side lengths of a triangle are given, the triangle can only have one shape.

congruent shapes

two figures that have corresponding congruent sides and angle measures (same exact size and shape)