New York City SHSAT 2017

Chapter 11 ...

Geometry Review HIGHLIGHTS Get an Overview of What Will Be on the Test Review the Geometry Content You Need to Know Practice Set ...

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Overview You’ll definitely see some geometry on the SHSAT. Like the rest of the math you’ll see on the test, SHSAT geometry will ...

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Geometry Content Review LINES AND ANGLES Line Segments Some of the most basic geometry problems on the SHSAT deal with line segm ...

Angles A right angle measures 90 degrees and is usually indicated in a diagram by a little box. The figure above is a right angl ...

Angles around a point add up to 360 degrees. In the figure above, a + b + c + d + e = 360. RECALL Angles around a point add up t ...

Parallel Lines When parallel lines are crossed by a transversal, iii. iv. Corresponding angles are equal (for example, a = e). A ...

TRIANGLES Triangles in General The three interior angles of any triangle add up to 180°. In this figure, x + 50 + 100 = 180, so ...

The length of one side of a triangle must be greater than the positive difference and less than the sum of the lengths of the ot ...

INTERIOR ANGLE MEASURE The total number of degrees inside a figure = 180(n − 2), where n = number of sides. Triangles—Area and P ...

The height is the perpendicular distance between the side that’s chosen as the base and the opposite vertex. In this triangle, 4 ...

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 ...