REVIEW rotations, reflections, Symmetry.

Matematicas

1. REVIEW Math 9th

2. Define and Apply Rotations A   rotation   is a rigid motion that turns a figure through an  angle of rotation   about a point P, such that each point and its image are the same distance from P.  All the angles with vertex P formed by a point and its image are congruent. The point P is called the  center of rotation

3. Lin Define and Apply Reflections A   reflection   is a transformation across a line, called the  line of reflection , such that the line of reflection is the perpendicular bisector of each segment joining each point and its image.

4. Define and Apply Symmetry A figure has   symmetry  if there is a transformation that maps the figure to itself. A figure has  line symmetry   if it can be reflected over a line so that the image coincides with the preimage. That line is called a  line of symmetry . A line of symmetry divides a plane figure into two reflected halves with the same size and shape. Two examples are shown. The  angle of rotational symmetry   is the smallest angle of rotation that maps a figure to itself.

5. Describe Symmetry in Regular Polygons

6. Define and Apply Dilations, Stretches, and Compressions The  angle of rotational symmetry   is the smallest angle of rotation that maps a figure to itself. A   stretch   changes the shape of a figure by a factor greater than 1 in one direction. A  compression   changes the shape of a figure by a factor greater than 0 and less than 1 in one direction. The  center of dilation   is the fixed point in the plane that does not change when the dilation is applied. The center can be on the image or elsewhere on the plane. Rays drawn from the center of dilation to the preimage will intersect corresponding points on the image. The  scale factor   k   of a dilation is the ratio of the length of a segment on the image to the length of the corresponding segment on the preimage. 

7. Transform figures with congruent corresponding parts. Conditional statement:   If a figure is obtained from another figure by a sequence of rigid motions, then the two figures are congruent. Converse:   If two figures are congruent, then one can be obtained from the other by a sequence of rigid motions.

8. Corresponding angles  and  corresponding sides   are located in the same position for polygons with an equal number of sides. You can write a congruence statement for two figures by matching the congruent corresponding parts. Two figures are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent . Conditional statement:  If all pairs of corresponding sides and all pairs of corresponding angles of two figures are congruent, then the figures are congruent. If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. Use Corresponding Parts to Show Figures Are Congruent

9. Three -Dimensional Figures Right solids   have an axis or lateral edges that are perpendicular to their base(s).   Oblique solids   have an axis or lateral edges that are not perpendicular to their base(s). A   prism   has two parallel congruent polygonal bases connected by lateral faces. Prisms are named by the shapes of their bases. A   cylinder   has two parallel congruent circular bases connected by a curved lateral surface. Its axis connects the centers of the bases. A   pyramid   has a polygonal base with triangular faces that meet at a vertex. A  cone  has a circular base and a curved surface that connects the edge of the circular base to its vertex. A  sphere  is the locus of points that are a fixed distance from its center. A  cross section   is the intersection of a three-dimensional figure and a plane.

10. Surface Areas of Prisms and Cylinders Surface area   is the total area of all faces and curved surfaces of a three-dimensional figure. The  lateral area   of a prism is the sum of the areas of the lateral faces. A  net   is a diagram of a three-dimensional figure arranged in such a way that the diagram can be folded to form the three-dimensional figure. A  right cone   is a cone whose axis is perpendicular to its base.  A  hemisphere   is half of a sphere. The surface area of a hemisphere is half the surface area of the related sphere plus the area of its circular base.