SAT Prep

A.) Terminology and Notation Lines / Rays / Segments Angles – Classification Straight - 180° Vertical - = Circle – 360°

Ex. In the figure, what is the value of a? Ex. In the figure below R, S, and T are all on line l. What is the average of a, b, c, d, and e? a b c d e l RST 3a3a c b (a+2b)

Ex. In the figure, what is the value of x? (3x+10) 5(x - 2)

Ex. Line m bisects AOB, what is the value of x? l m k O x 130 A B

B.) Parallel Lines – 4 pair of congruent angles. – Know angle theorems. Perpendicular to Parallels Thm. Ex. In the figure below l // m, find the value of x. x 140l m k

Ex. Given AB // CD in the figure below, find the value of x. Ex. Given the figure below l // m, find the value of a + b. x 37 BA DC 45 a b l m

IN GENERAL – Sum of angles of all polygons = (n-2)180 Sum of the exterior angles = 360 degrees A.) Classification by angles :AcuteRightObtuse by sides:ScaleneIsoscelesEquilateral

Ex. Given the figure below, find x. Ex. Given the figure below, find a x a 75 45

B.) Theorems 1.) Exterior Angle Thm. 2.) Largest Side is opposite Largest Angle. 3.) Smallest side GREATER THAN the DIFF. of other two. 4.) Largest side LESS THAN the SUM of the other two. 5.) PYTHAGOREAN THEOREM – Know Triples Esp. 3 – 4 – 5 and multiples

C.) Special Right Triangles – 45º – 45º – 90º 30º – 60º – 90º 45 s s s x x 2x2x 60 30

Ex. What is the area of a square whose diagonal is 10? Ex. In the diagram, if BC =, what is the value of CD? C D B

Ex. If the lengths of two sides of a triangle are 6 and 7, what are the possible values of the third side?

D.) AREA of a TRIANGLE 1.) ½ bh 2.) 3.) Equilateral = Ex. Find the area of an equilateral triangle whose side is 10.

Ex. An equilateral triangle with an area of has what perimeter?

Ex. A triangular traffic island with a flat surface is formed by the intersection of three streets. Two of the sides of the islands have lengths of 6.4 meters and 10.8 meters. If the measure of the angle between these two sides is 55º, what is the area, in square meters, of the triangular surface of the island?

E.) SIMILAR TRIANGLES 3 pairs of = angles 3 pair of proportional sides Ex. Given the figure below, find BC AB C ED

Sum of angles = 360 degrees A.) Special Quads. 1.) Parallelograms – Opp. Sides = Opp. Sides // Opp. Angles = Cons. Angles supplementary 2 diagonals bisect each other

2.) Rectangles – All properties of // -ograms Diagonals = All 4 angles = 90 degrees 3.) Squares – All properties of rectangles All four sides = B.) Area formulas – Parallelogram = bh Rectangle = lw Square = s 2 or ½ d 2

Ex. What is the length of each side of a square whose diagonal is 10?

Ex. The length of a rectangle is twice the width. If the perimeter of the rectangle is the same as the perimeter of a square with side 6, what is the square of the length of a diagonal of the rectangle?

Ex. If AB = BC and DB = 5, then the area of ABCD =. AB CD