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)

Tessellating Quadrilaterals Conjecture

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

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