# Geometry Ch. 4

## 36 terms

### Acute triangle

Three acute angles

### Equiangular triangle

Three congruent acute angles

One right angle

One obtuse angle

### Equilateral triangle

Three congruent sides

### Isosceles triangle

At least two congruent sides

### Scalene triangle

No congruent sides

### Vertices

a corner of a polygon

### Triangle sum theorem

The sum of the angle measures of a triangle is 180 degrees

### Corollary

A theorem whose proof follows directly from another theorem

### Interior

The set of all points inside the figure

### Exterior

The set of all points outside the figure

### Interior angle

Is formed by two sides of an angle

### Exterior angle

Is formed by one side of a triangle and the extension of the adjacent side

### Remote Interior angles

An interior angle that is not adjacent to the exterior angle

### Exterior angle theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles

### Third angle theorem

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

Ok

### Triangle rigidity

A shortcut for proving two triangles congruent

### Included angle

An angle formed by two adjacent sides of a polygon

### Side-Side-Side postulate (SSS)

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent

### Side-Angle-Side postulate (SAS)

If two sides and the included angle of one triangle are congruent to two sides and and the included side of another triangle, then the triangles are congruent.

### Included Side

The common side of two consecutive angles in a polygon

### Angle-Side-Angle postulate (ASA)

If two angles and the included side of one triangle are congruent to two angles and a included side of another triangle, then the triangles are congruent

### Angle-Angle-Side postulate (AAS)

If two angles and a nonincluded side of one angle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent

### Hypotenuse-Leg postulate (HL)

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent

### CPCTC

An abbreviation for "Corresponding parts of congruent triangles are congruent" It can be used as a justification in a proof after you have proven two triangles congruent

### Coordinate proof

A style of proof that uses coordinate geometry and algebra

### Legs

The congruent sides in a isosceles triangle

### Vertex angle

The angle formed by the legs

### Base

The side opposite to the vertex angle

### Base angles

The two angles that have the base as a side

### Isosceles triangle theorem

If two sides of a triangle are congruent, then the angles opposite to the sides are congruent

### Converse of Isosceles triangle theorem

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

### Equiangular triangle corallary

If a triangle is equiangular, then it is equilateral

### Auxiliary line

A line that you can add to a proof that helps you prove something