SAT Geometric Perception是什么?这种题怎么解?

SAT Geometric Perception是什么?这种题怎么解?
SAT Geometric Perception是什么?这种题怎么解?

SAT Geometric Perception是什么?这种题怎么解?
这是指SAT的几何概念.主要包括：
Points and Lines
　　There is a unique line that contains any two distinct points. Therefore, in the following diagram, line l is the only line that contains both point A and point B.
　　The midpoint of a line segment is the point that divides it into two segments of equal length. The diagram below shows the midpoint M of line segment AB.
　　Because M is the midpoint of AB, you know that AM=MB.
Angles in the Plane
　　Vertical angles and supplementary angles. Two opposite angels formed by two intersecting lines are called vertical angles. Vertical angles have the same measure. Two angles whose measures have a sum of 180°are called supplementary angles.
　　Parallel lines. When two parallel lines are crossed by another line, all acute angles are equal, and all obtuse angles are equal. Also, every acute angle is supplementary to every obtuse angle (that is, they add up to 180°).
　　Right angles and perpendicular lines. A right angle is an angle with a measure of 90°. If two lines intersect and one of the four angles formed is aright angle, the lines are perpendicular. In this case, all four angles that are formed are right angles.
Triangles
　　The sum of the measures of the three interior angles in any triangle is 180°.
　　An exterior angle of a triangle is equal to the sum of the remote interior angles.
　　The three exterior angles of a triangle add up to 360°.
　　Equilateral triangles: The three sides of an equilateral triangle (a, b, c) are equal in length. The three angles are also equal, and they each measure 60°.
　　Isosceles triangles: An isosceles triangle is a triangle with two sides of equal length. The angles opposite the equal sides are also equal.
　　Right triangles and Pythagorean Theorem: A right triangle is a triangle with a right angle. Pythagorean Theorem: the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The hypotenuse is the longest side of the triangle and is opposite the right angle. The other two sides are usually referred to as legs. If c represents the length of hypotenuse, and a and b are the lengths of two legs, respectively, then the Pythagorean theorem leads to the equation:
　　a2+b2=c2
　　Special right triangles:(30°-60°-90°, 45°-45°-90°, 3-4-5)
　　◆ 30°-60°-90° Triangles: the lengths of the sides of a 30°-60°-90°triangle are in the ratio of x:x3:2x.
　　Short leg=x
　　 Long leg=x3
　　 Hypotenuse=2x
　　◆ 45°-45°-90° Triangles: the lengths of the sides of a 45°-45°-90° triangle are in the ratio of x:x:x2.
　　Short leg=x
　　Long leg=x
　　Hypotenuse=x2
　　◆ 3-4-5 Triangles: The sides of a 3-4-5 right triangle are in the ratio of 3x:4x:5x. For example, if x=5, the sides of the triangle have lengths 15, 20 and 25.
　　Congruent triangles: are triangles that have the same size and shape. Two triangles are congruent if any of the following is true:
　　◆ Each pair of corresponding sides has the same length.
　　◆ Two pairs of corresponding sides each have the same length, and the angles formed by these sides have the same measure.
　　◆ One pair of corresponding sides has the same length, and two pairs of corresponding angles each have the same measure.
　　Similar triangles. Similar triangles have the same shape. Each corresponding angles are equal and corresponding sides are directly proportional.
　　The triangle inequality. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
　　Parallelograms. A parallelogram, a special quadrilateral, has two pairs of parallel sides. Opposite sides are equal. Opposite angels are equal. Consecutive angles add up to 180 degrees.
　　Rectangles and Squares. A rectangle is a special case of a parallelogram with four right angles. A square is a special case of a rectangle in which the lengths of all the sides are equal.
Areas and Perimeters
　　Rectangle: Area=length×width, Perimeter=2(length+width)
　　Square: Area=(side)2, Perimeter=4×(side)
　　Triangle: Area=12(base•height), Perimeter=add up three sides
　　Parallelogram: Area=length×height
　　Polygons. The sum of the measures of the interior angles of a polygon=(n-2)×180, where n (≥3) is the number of sides. The sum of the measures of the exterior angles of any polygon is 360 degrees.
Circles
　　Diameter and Radius. The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle. The radius of a circle is a line segment extending from the center of the circle to a point on the circle.
　　Diameter=2×Radius
　　Circumference and Area. The circumference is the distance around a circle:
　　Circumference=2πr
　　where r is the radius of the circle. The area of a circle is equal to π times the square of the radius:
　　Area=πr2
　　Arc. An arc is a piece of the circumference. In the figure above, the points on the circle from A to B form an arc. If r is the radius and n is the degree measure of the arcs central angle, then the formula to figure out the length of an Arc is:
　　Length of an Arc =n3602πr
　　Tangent to a circle. A tangent to a circle is a line that intersects the circle at exactly one point. In the figure, line AC is a tangent. A tangent to a circle is always perpendicular to the radius that contains the one point of the line that touches the circle. In this case, OA⊥AC.
　　Central angle, arc, area proportional theorem. For any pie slice of a circle, the central angle, arc, and area are in proportion to the whole circle. For example, if n equals to 60 degrees in the figure above, n360=60360=16, so arc AB is 16 of the circumference, and pie slice AOB is 16 of the total area.
　　Solid figures and volumes. The basic types of solids include cubes, rectangular solids, prisms, cylinders, cones, spheres and pyramids.
　　Cubes and Rectangular solids. Every edge of a cube has the same length. If the edge length of a cube is s, then the volume of the cube is s3. In a rectangular solid, the length, width and height may be different. The volume is given by the formula:
　　V=length×width×height.
　　Prisms and Cylinders. A right prism is a solid in which two congruent polygons are joined by rectangular faces that are perpendicular to the polygons. The congruent polygons are called the bases of the prism, and the length of an edge joining the polygons is called the height. The volume of a prism is given by the product of its height and the area of its base. A right circular cylinder is a solid in which two congruent circles are joined by a curved surface that meets the circles at a right angle. The volume of a right circular cylinder is given by the formula: V=πr2h, where r is the radius of the circular base, and h is the height of the cylinder.
　　Spheres, Cones and Pyramids. A sphere is the solid analogue of a circle. All radii of a sphere are equal. A circular cone has a circular base, which is connected by a curbed surface to its vertex. If the line from the vertex of the circular cone to the center of its base is perpendicular to the base, then the cone is called a right circular cone. A pyramid has a base that is a polygon, which is connected by triangular faces to its vertex. If the base is a regular polygon and the triangular faces are all congruent isosceles triangles, then the pyramid is called a regular pyramid.
　　Surface area. To find the surface area of a solid, just find the area of each face of the solid, and then add them up.
　　Geometric Perception. The SAT may ask you questions that require you to visualize a plane figure or a solid from different views or orientations. These are questions in geometric perception.
　　Slopes. Every line has a slope. The slope is simply the Rise divided by the Run.
　　Using two points to find the slope:
　　slope=riserun=y2-y1x2-x1
　　Using an equation to find the slope: put the equation into the slope-intercept formula: y=mx+b, then the slope is m.
　　If two lines in the xy-plane are parallel exactly, their slopes are equal.
　　If two lines in the xy-plane are perpendicular, the product of their slopes is -1.
　　Line equations
　　Slope-intercept formula: y=mx+b, where m is the slope and b is the y-intercept.
　　Slope-point formula: y-y0=m(x-x0), where P(x0,y0) is a point on the line, and m is the slope.
　　Two-points formula: y-y1y2-y1=x-x1x2-x1, where P(x1,y1) and P(x2,y2) are two points on the line.
　　Midpoint formula, Distance formula
　　Midpoint Formula. If A(x1,y1) and B(x2,y2) are two points in the xy-plane, the midpoint (xm,ym) of the line segment AB is given by the formula:
　　Midpoint (xm,ym)=x1+x22,y1+y22
　　Distance Formula. If A(x1,y1) and B(x2,y2) are two points in the coordinate plane, the distance between them is given by the formula:
　　AB=(x2-x1)2+(y2-y1)2
　　Transformations. Transformations include translations, rotations, and reflections.
　　Translations: a translation moves a shape certain units up, down, to the left, or to the right without any rotation or reflection.
　　Rotations: rotating an object means turning it around a point, which is called the center of rotation.
　　Reflections: reflecting an object means to produce its mirror image with respect to a line, which is called the line of reflection.