NCSSM placement Test Practice Questions and
Correct Verified Answers
Angles - ✔✔acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles
are between 90 and 180 degrees. Straight angles are 180 degrees and reflex angles are greater
than 180 degrees.
Adjacent angles - ✔✔share a common vertex, a common side, but not common interior
points.
Complementary angles - ✔✔2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles - ✔✔2 angles when added together that equal 180 degrees.They do not
have to be adjacent angles.
Vertical angles - ✔✔vertical angles are congruent.
Alternate interior angles - ✔✔alternate interior angles are congruent.
Corresponding angles - ✔✔corresponding angles are congruent.
Sum of the angles in a triangle - ✔✔the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides - ✔✔scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles - ✔✔acute triangles have 3 acute angles.
,right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle - ✔✔the exterior angle of a triangle equals the sum of the 2
opposite interior angles.
Isosceles triangles - ✔✔sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem - ✔✔the sum of 2 sides of a triangle must be greater than the 3rd
side.
Mid segment of a triangle - ✔✔a mid segment connects the midpoint of 2 sides of a triangle
and is equal to ½ the side not containing the 2 midpoints.
Median - ✔✔bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector - ✔✔bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude - ✔✔makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector - ✔✔bisects and makes a right angle with a side of a triangle.They
meet in a triangle at a point called the circumcenter.
Similar triangles - ✔✔angles in similar (∼) triangles are congruent.
,sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - ✔✔need only 2 angles to be congruent to probe 2 triangles similar.
Proving triangles congruent - ✔✔can not be angle angle side (A.S.S.) or side side
angle(S.S.A.).
C.P.C.T.C. - ✔✔corresponding parts of congruent triangles are congruent.
Pythagorean theorem - ✔✔a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent - ✔✔hypotenuse leg.
Right triangle ratios - ✔✔
Slope - ✔✔from left to right. up the hill is positive slope. down the hill is negative slope. a
horizontal line has 0 slope and a verical line as an undefined slope.
Point slope form of a line - ✔✔y minus y one equals slope (m) times x minus x one.
Slope intercept form of a line - ✔✔y equals slope (m) times x plus the y intercept (b)
Slope formula - ✔✔y two minus y one divided by x two minus x one.
rise over run.
, Distance formula - ✔✔the square root of x two minus x one squared plus y two minus y one
squared.
Midpoint formula - ✔✔x one plus x two divided by two is the x coordinate.
y one plus y two divided by two is the y coordinate.
Find the endpoint of a line given the midpoint and the other endpoint - ✔✔the integers added
to the coordinates of C to get the coordinates of M are added to the coordinates of M to get the
coordinates of D.
Finding the slope and y intercept of a line - ✔✔y must be positive and isolated on one side of
the equation.
Slopes of parallel lines - ✔✔have the same slope and a different y intercept.
Slopes of perpendicular lines - ✔✔the slopes are negative reciprocals.
to find the negative reciprocal make the slope a fraction, flip it, and change the sign.
Parallel and perpendicular lines - ✔✔
Axis of symmetry - ✔✔the equation for axis of symmetry is x equals negative b divided by
two times a.
Surface area of a cylinder - ✔✔2 times pi times radius times the sum of the height and radius.
Volume of a cylinder - ✔✔pi times radius squared times the height.
Surface area of a rectangular prism - ✔✔2 times the sum of the length times the width, the
length times the height. and the width times the height.
Correct Verified Answers
Angles - ✔✔acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse angles
are between 90 and 180 degrees. Straight angles are 180 degrees and reflex angles are greater
than 180 degrees.
Adjacent angles - ✔✔share a common vertex, a common side, but not common interior
points.
Complementary angles - ✔✔2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles - ✔✔2 angles when added together that equal 180 degrees.They do not
have to be adjacent angles.
Vertical angles - ✔✔vertical angles are congruent.
Alternate interior angles - ✔✔alternate interior angles are congruent.
Corresponding angles - ✔✔corresponding angles are congruent.
Sum of the angles in a triangle - ✔✔the 3 angles of a triangle add up to 180 degrees.
Triangles classified by sides - ✔✔scalene triangles have no equal sides.
isosceles triangles have at least 2 equal sides.
equilateral triangles have 3 equal sides.
Triangles classified by angles - ✔✔acute triangles have 3 acute angles.
,right triangles have a 90 degree and 2 acute angles.
obtuse triangles have an obtuse and 2 acute angles.
Exterior angle of a triangle - ✔✔the exterior angle of a triangle equals the sum of the 2
opposite interior angles.
Isosceles triangles - ✔✔sides opposite congruent angles are congruent.
angles opposite congruent sides are congruent.
Triangle inequality theorem - ✔✔the sum of 2 sides of a triangle must be greater than the 3rd
side.
Mid segment of a triangle - ✔✔a mid segment connects the midpoint of 2 sides of a triangle
and is equal to ½ the side not containing the 2 midpoints.
Median - ✔✔bisects the opposite side into 2 congruent line segments.
they meet in a triangle at a point called the centroid.
median segments are in a ratio of 2 to 1.
Angle bisector - ✔✔bisects an angle into 2 congruent angles.
they meet in a triangle at a point called the incenter.
Altitude - ✔✔makes a right angle with the opposite side.
they meet in a triangle at a point called the orthocenter.
Perpendicular bisector - ✔✔bisects and makes a right angle with a side of a triangle.They
meet in a triangle at a point called the circumcenter.
Similar triangles - ✔✔angles in similar (∼) triangles are congruent.
,sides are in proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - ✔✔need only 2 angles to be congruent to probe 2 triangles similar.
Proving triangles congruent - ✔✔can not be angle angle side (A.S.S.) or side side
angle(S.S.A.).
C.P.C.T.C. - ✔✔corresponding parts of congruent triangles are congruent.
Pythagorean theorem - ✔✔a squared plus b squared equals c squared.
the hypotenuse is always c.
Proving right triangles congruent - ✔✔hypotenuse leg.
Right triangle ratios - ✔✔
Slope - ✔✔from left to right. up the hill is positive slope. down the hill is negative slope. a
horizontal line has 0 slope and a verical line as an undefined slope.
Point slope form of a line - ✔✔y minus y one equals slope (m) times x minus x one.
Slope intercept form of a line - ✔✔y equals slope (m) times x plus the y intercept (b)
Slope formula - ✔✔y two minus y one divided by x two minus x one.
rise over run.
, Distance formula - ✔✔the square root of x two minus x one squared plus y two minus y one
squared.
Midpoint formula - ✔✔x one plus x two divided by two is the x coordinate.
y one plus y two divided by two is the y coordinate.
Find the endpoint of a line given the midpoint and the other endpoint - ✔✔the integers added
to the coordinates of C to get the coordinates of M are added to the coordinates of M to get the
coordinates of D.
Finding the slope and y intercept of a line - ✔✔y must be positive and isolated on one side of
the equation.
Slopes of parallel lines - ✔✔have the same slope and a different y intercept.
Slopes of perpendicular lines - ✔✔the slopes are negative reciprocals.
to find the negative reciprocal make the slope a fraction, flip it, and change the sign.
Parallel and perpendicular lines - ✔✔
Axis of symmetry - ✔✔the equation for axis of symmetry is x equals negative b divided by
two times a.
Surface area of a cylinder - ✔✔2 times pi times radius times the sum of the height and radius.
Volume of a cylinder - ✔✔pi times radius squared times the height.
Surface area of a rectangular prism - ✔✔2 times the sum of the length times the width, the
length times the height. and the width times the height.
