SOL 7.6, 7.7, 7.5, 7.8 SOL 7.6: The student will determine whether plane figures—quadrilaterals and triangles—are similar and write proportions to express the relationships between the corresponding sides of similar figures. Congruent polygons have the same size and same shape. Similar polygons have the same shape but different sizes. Quadrilaterals—4 sided polygons Triangle—3 sided polygons Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. Ex) congruent Ex) Similar Two shapes are similar if they are proportional. To find out if they are proportional, use corresponding parts. 4 8 Ex) = 6 12 Cross multiply: 4 x 12 = 48 8 x 6 = 48 These products are equal so these two rectangles are proportional therefore they are similar. You can find the missing side lengths by setting up a proportion with corresponding sides. 𝑥 6 = 35 7 7x = 210 x = 30 Congruent polygons are similar polygons for which the ratio of the corresponding sides 1:1. The traditional notation for marking congruent angles is to use a curve for each angle. Denote which angles are congruent with the same number of curved lines. Congruent sides are denoted with the same number of hatch (little lines) marks on each congruent side. SOL 7.7: The student will compare and contrast the following quadrilaterals based on properties: parallelogram, rectangle, square, rhombus, and trapezoid. A quadrilateral is a closed plane figure with four sides that are line segments. Ex) A parallelogram is a quadrilateral whose opposite sides are parallel and opposite angles are congruent. Ex) A rectangle is a parallelogram with four right angles. The diagonals of are rectangle are the same length and bisect each other. A rectangle has opposite sides congruent. (A square is always a rectangle but a rectangle may not be a square.) Ex) A square is a rectangle with four congruent sides whose diagonals are perpendicular. A square has four right angles. It is also a parallelogram and rhombus. Ex) A rhombus is a parallelogram with four congruent sides whose diagonals bisect each other and intersect at right angles. Ex) A trapezoid is a quadrilateral with exactly one pair of parallel lines. A trapezoid with congruent, nonparallel sides is called an isosceles trapezoid. Ex) SOL 7.5: The student wil a) Describe volume and surface area of cylinders b) Solve practical problems involving the volume and surface area of rectangular prisms and cylinders c) Describe how changing one measured attribute of a rectangular prism affects its volume and surface area. Volume—the measure of the amount of space inside a figure Surface Area—the total area of the exterior surfaces of a solid figure **use your formula sheets Figure out the shape and the correct formula. Draw your box and identify the attributes needed to solve the formula Plug in the correct numbers. Solve the equations (Volume has a little 3 behind it and surface area has a little 2.) SOL 7.8: The student, given a polygon in the coordinate plane, will represent transformations (reflections, dilations, rotations, and translations) by graphing in the coordinate plane. A transformation is a change in the figure. A translation is a slide of the figure in which all the points on the figure move the same distance in the same direction. A reflection is a flip across a line in the plane. A rotation is a turn of the figure around a fixed point. A dilation is a change in the size of a figure. It can be either an enlargement (bigger) or a reduction (smaller). The image is the polygon after a transformation has been performed. The preimage is the polygon you started with. ***See notes for these!