# Triangle Congruence

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Triangle Congruence

## 1. Congruence and Transformations

### 1.1. dilation

1.1.1. the action or condition of becoming or being made wider, larger, or more open.

### 1.2. isometry

1.2.1. An isometry is a transformation that preserves length, angle measure, and area. Because of these properties, an isometry produces an image that is congruent to the preimage.

### 1.3. rigid transformation

1.3.1. A rigid transformation is another name for an isometry.

## 2. Classifying Triangles

### 2.1. acute triangle

2.1.1. Three acute angles (less than 90°)

### 2.2. equiangular triangle

2.2.1. Three congruent angles (angles 60°)

### 2.3. right triangle

2.3.1. One right angle (90°)

### 2.4. obtuse triangle

2.4.1. One obtuse angle (greater than 90°)

### 2.5. equilateral triangle

2.5.1. Three congruent sides

### 2.6. isosceles triangle

2.6.1. At least two congruent sides

### 2.7. scalene triangle

2.7.1. No congruent sides

## 3. Angle Relationships in Triangles

### 3.1. auxiliary line

3.1.1. An auxiliary line is a line that is added to a figure to aid in a proof.

### 3.2. corollary

3.2.1. An auxiliary line is a line that is added to a figure to aid in a proof.

### 3.3. interior

3.3.1. The interior is the set of all points inside the figure.

### 3.4. exterior

3.4.1. The exterior is the set of all points outside the figure.

### 3.5. interior angle

3.5.1. An interior angle is formed by two sides of a triangle.

### 3.6. exterior angle

3.6.1. An exterior angle is formed by one side of the triangle and extension of an adjacent side.

### 3.7. remote interior angle

3.7.1. A remote interior angle is an interior angle that is not adjacent to the exterior angle.

## 4. Congruent Triangles

### 4.1. corresponding angles

4.1.1. Corresponding angles and corresponding sides are in the same position in polygons with an equal number of sides.

### 4.3. congruent polygons

4.3.1. Two polygons are congruent polygons if and only if their corresponding sides are congruent.

## 5. Triangle Congruence: SSS and SAS

### 5.1. triangle rigidity

5.1.1. The property of triangle rigidity gives you a shortcut for proving two triangles congruent.

### 5.2. included angle

5.2.1. An included angle is an angle formed by two adjacent sides of a polygon.

## 6. Triangle Congruence: ASA, AAS, and HL

### 6.1. included side

6.1.1. An included side is the common side of two consecutive angles in a polygon.