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Mathematics 217

Chapters 13 - 14

Isometry Any rigid motion that preserves length or distance is an isometry. It can be shown that under any isometry, the image of a line is a line, the image of a circle is a circle, and the images of parallel lines are parallel lines.
Translation A translation is a motion of a plane that moves every point of the plane a specified distance in a specified direction along a straight line.
Translation in a coordinate system A translation is a function from the plane to the plane such that to every point (x,y) corresponds the point (x + a, y + b), where a and b are real numbers.
Rotation A rotation is a transformation of the plane determined by holding one point, the center, fixed and rotating the plane about this point by a certain amount in a certain direction.
Special rotation A rotation of 360° about a point moves any point and hence any figure onto itself. Such a transformation is an identity transformation. Any point may be the center of such a rotation. A rotation of 180° about a point is a half-turn.
Slopes of perpendicular lines We can use transformations to investigate various mathematical relationships, including the slopes between two non-vertical perpendicular lines. If we rotate a line in the plane by 90 degrees about a point on the line, we have a perpendicular line.
Reflection A reflection in a line ℓ is a transformation of a plane that pairs each point P of the plane with a point P′ in such a way that ℓ is the perpendicular bisector of PP′, as long as P is not on ℓ.
Glide reflection Glide reflection, is a transformation consisting of a translation followed by a reflection in a line parallel to the slide arrow.
Areas on a geoboard (dot paper) Addition method divide an area into smaller pieces and then add the areas.
Areas of a geoboard (dot paper) Rectangle method is to construct a rectangle encompassing the entire figure and then subtract the areas of the unshaded regions.
Pythagorean theorem Given a right triangle with legs a and b and hypotenuse c, c2 = a2 + b2.
45 degrees 45 degrees 90 degrees right triangle The length of the hypotenuse in a 45°-45°-90° (isosceles) right triangle is the square root of 2 times the length of a leg.
30 degrees 60 degrees 90 degrees right triangle In a 30°-60°-90° right triangle, the length of the hypotenuse is twice the length of the leg opposite the 30° angle (the shorter leg).
Created by: marianhood