# Discovering Geometry Chapter 7 Conjectures

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### Reflection Line Conjecture

The line of reflection is the perpendicular bisector of every
segment joining a point in the original figure with its image. (Lesson 7.1)

### Coordinate Transformations Conjecture

The ordered pair rule (x, y) → (-x, y) is a reflection over the y-axis. The ordered pair rule (x, y) → (x, -y) is a reflection over the x-axis. The ordered pair rule (x, y) → (-x, -y) is a rotation about the origin. The ordered pair rule (x, y) → (y, x) is a reflection over y = x. (Lesson 7.2)

### Minimal Path Conjecture

If points A and B are on one side of line L, then the minimal path from point A to line L to point B is found by reflecting point B over line L, drawing segment AB', then drawing segments AC and CB where point C is the point of intersection of segment AB' and line 􏰆. (Lesson 7.2)

### Reflections over Parallel Lines Conjecture

A composition of two reflections over two parallel lines is equivalent to a single translation. In addition, the distance from any point to its second image under the two reflections is twice the distance between the parallel lines. (Lesson 7.3)

### Reflections over Intersecting Lines Conjecture

A composition of two reflections over a pair of intersecting lines is equivalent to a single rotation. The angle of rotation is twice the acute angle between the pair of intersecting reflection lines. (Lesson 7.3)

### Tessellating Triangles Conjecture

Any triangle will create a monohedral tessellation. (Lesson 7.5)

Any quadrilateral will create a monohedral tessellation. (Lesson 7.5)

Example: