New York City SHSAT 2017

Similar triangles have the same shape: corresponding angles are equal, and corresponding sides are proportional. The triangles s ...

Equilateral triangles are triangles in which all three sides are equal. Since all the sides are equal, all the angles are also e ...

The Pythagorean Theorem (leg 1 )^2 + (leg 2 )^2 = (hypotenuse)^2 If one leg is 2 and the other leg is 3, and the hypotenuse is c ...

If a right triangle’s leg-to-leg ratio is 3:4, or if the leg-to-hypotenuse ratio is 3:5 or 4:5, it’s a 3-4-5 triangle, and you d ...

Side-Angle Ratios The sides of a 30-60-90 triangle are in a ratio of You don’t need to use the Pythagorean theorem. If the hypot ...

Be on the lookout for “special” right triangles. Recognizing them can save you time and gain you points on the SHSAT. The sides ...

QUADRILATERALS The perimeter of a polygon is the sum of the lengths of its sides. The perimeter of the quadrilateral in the figu ...

A square is a rectangle with four equal sides. The formula for the area of a square is Area = (Side)^2 In the diagram above, s = ...

A trapezoid is a quadrilateral with one pair of parallel sides. The formula for the area of a trapezoid is In the diagram above, ...

Exercise xiii. What is the area of the parallelogram above? xiv. What is the area of the trapezoid above? xv. The rectangles abo ...

CIRCLES A circle is a figure for which each point is an equal distance from its center. In the diagram, O is the center of the c ...

There are 360 degrees in a circle. The circumference of a circle is the distance around it. It is equal to πd, or 2πr. In this e ...

OZ = 4 WX = OX = xvii. Radius = 8 Circumference = xviii. xix. Area = 16π ...

ESTIMATING Π π is approximately 3.14, but all you need to remember is that it’s a little more than 3. Radius = ...

COORDINATE GEOMETRY The diagram above represents the coordinate axes—the perpendicular “number lines” in the coordinate plane. T ...

Plotting Points If you were asked to graph the point (2, −3) you would start at the origin and count 2 units to the right and 3 ...

To use two points to find the slope of a line, use the following formula: In general, the slope of a line connecting the points ...

In the figure above, the length of segment AB is |7 − 1| = 6. The length of segment CD is |0 − (−4)| = 4. REMEMBER Length is alw ...

xxii. Find the lengths of the line segments graphed above: 1. AB = 2. CD = 3. EF = ...

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