CRACKING GEOMETRY CRACKING GEOMETRY Degrees and Angles Triangles

CRACKING GEOMETRY

CRACKING GEOMETRY �Degrees and Angles �Triangles �Circles �Rectangles and squares �Tips and Techniques

Degrees and Angles �A circle contains 360 degrees �When you think about angles, remember circles. �A line is a 180 degree angle. �When two lines intersect, four angles are created. The sum of their measures is 360 degrees.

Degrees and Angles �When two parallel lines are cut by a third line, the small angles are equal, the big angles are equal, and the sum of a big angle and a small angle is 180 degrees. �______________________________

Triangles �Every triangle contains 180 degrees. �An equilateral triangle is one in which: � All three angles are equal (60 degrees). �All three sides are equal in length.

Triangles �An isosceles triangle is one in which: �Two of the sides are of equal length. �The two angles opposite the equal sides are equal in measure.

Triangles �A right triangle is one in which one of the angles is a right triangle (90 degrees).

Triangles �The perimeter of a triangle is the sum of its sides.

Triangles ½ �The area of a triangle is 1/2 bh. �The height must form a right angle to the base.

Triangles �The Pythagorean theorem states that in a right triangle: �The square of the hypotenuse = the sum of the squares of the other two sides. �Remember ETS’s favorite Pythagorean triplets (3 -4 -5 and 5 -1213).

Triangles �Remember the other special triangles: 45 -45 -90 and 30 -60 -90 �Similar triangles have the same angles and their lengths are in proportion.

Circles �The circumference of a circle is 2 pr or pd where r is the radius of the circle and d is the diameter. �The area of a circle is pr 2, where r is the radius of the circle. �The tangent touches a circle at one point �Any radius that touches that tangent forms a 90 degree angle.

Rectangles and Squares �The perimeter of a rectangle is the sum of the length of its sides. �The area of a rectangle is length x width. �A square is a rectangle whose four sides are all equal in length. �Any polygon can be divided into triangles.

Rectangles and Squares �The volume of a rectangular solid is length x width x height. �The formulas to compare the volume of other three dimensional figures are supplied in the instructions at the front of every math section on the SAT.

Rectangles and Squares �You must know how to locate points on a grid.

Other Geometry Stuff �When you encounter a geometry problem on the SAT, ballpark the answer before trying to work it out. �You need to be familiar with the size of certain common angles. �You can use your test booklet as a ruler.

Other Geometry Stuff �Most SAT diagrams are drawn to scale. �Use your eyes before you use your pencil. Try to eliminate impossible answers. �When a diagram is not drawn to scale, redraw it.

Other Geometry Stuff �When no diagram is provided…make your own. �When an incomplete diagram is provided…complete it. �When info is missing from a diagram, ballpark and plug in.

Other Geometry Stuff �Some extremely difficult SAT geometry problems can be solved quickly but you will have to stay on your toes. �The way to do this is to ask yourself 3 questions: 1. What info have I been given? 2. What info have I been asked to find? 3. What is the relationship between