NCSSM placement test questions with g g g g
correct answers
g g
Tangent - intersects a circle in only 1 place.
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Secant - intersects a circle in 2 places.
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Intersection of a tangent and a radius - form right angles when they intersect.
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Equation of a circle - x minus h squared plus y minus k squared equals radius squared.
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Circumference of a circle - 2 times pi times radius or pi times diameter.
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Area of a circle - pi times radius squared.
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Central angle - is equal to its intercepted arc.
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Inscribed angle - is equal to ½ its intercepted arc.
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Angle formed by 2 chords intersecting in a circle - is equal to the sum of the arcs
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divided by 2.
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Angle formed by 2 secants - is equal to the major arc minus the minor arc divided by 2.
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Angle formed by a secant and a tangent - is equal to the major arc minus the minor arc
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divided by 2.
g g g
Angle formed by two tangents - is equal to the major arc minus the minor arc divided by
g g g g g g g g g g g g g g g g g
2.
g
Lengths of 2 intersecting chords - part of the first chord times the other part of the first
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chord equals a part of the second chord times the other part of the second chord.
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Lengths of an intersecting diameter and chord that meet at right angles (perpendicular) -
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if a diameter meets a chord at a right angle (perpendicular), the diameter divides the
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chord into 2 equal parts.
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Lengths of 2 intersecting secants - the whole length of the first secant times the outside
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length of the first secant equals the whole length of the second secant times the outside
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length of the second secant.
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,Lengths of an instersecting secant and tangent - the whole length of the first secant
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times the outside length of the first secant equals the length of the tangent squared.
g g g g g g g g g g g g g g g
Lengths of intersecting tangents - Tangents to a circle sharing a common vertex are
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equal.
g
Angles - acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse
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angles are between 90 and 180 degrees. Straight angles are 180 degrees and reflex
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angles are greater than 180 degrees.
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Adjacent angles - share a common vertex, a common side, but not common interior
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points.
g
Complementary angles - 2 angles when added together that equal 90 degrees.
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They do not have to be adjacent angles.
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Supplementary angles - 2 angles when added together that equal 180 degrees.They do
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not have to be adjacent angles.
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Vertical angles - vertical angles are congruent.
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Alternate interior angles - alternate interior angles are congruent.
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Corresponding angles - corresponding angles are congruent. g g g g g g
Sum of the angles in a triangle - the 3 angles of a triangle add up to 180 degrees.
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Triangles classified by sides - scalene triangles have no equal sides.
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isosceles triangles have at least 2 equal sides.
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equilateral triangles have 3 equal sides. g g g g g
Triangles classified by angles - acute triangles have 3 acute angles.
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right triangles have a 90 degree and 2 acute angles.
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obtuse triangles have an obtuse and 2 acute angles.
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Exterior angle of a triangle - the exterior angle of a triangle equals the sum of the 2
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opposite interior angles.
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Isosceles triangles - sides opposite congruent angles are congruent.
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angles opposite congruent sides are congruent.
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Triangle inequality theorem - the sum of 2 sides of a triangle must be greater than the
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3rd side.
g g
, Mid segment of a triangle - a mid segment connects the midpoint of 2 sides of a triangle
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and is equal to ½ the side not containing the 2 midpoints.
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Median - bisects the opposite side into 2 congruent line segments.
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they meet in a triangle at a point called the centroid.
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median segments are in a ratio of 2 to 1.
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Angle bisector - bisects an angle into 2 congruent angles.
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they meet in a triangle at a point called the incenter.
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Altitude - makes a right angle with the opposite side.
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they meet in a triangle at a point called the orthocenter.
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Perpendicular bisector - bisects and makes a right angle with a side of a triangle.They
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meet in a triangle at a point called the circumcenter.
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Similar triangles - angles in similar (∼) triangles are congruent.
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sides are in proportion.
g g g
angles are in a proportion of one to one. (1:1)
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Proving triangles similar - need only 2 angles to be congruent to probe 2 triangles
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similar.
g
Proving triangles congruent - can not be angle angle side (A.S.S.) or side side
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angle(S.S.A.).
g
C.P.C.T.C. - corresponding parts of congruent triangles are congruent.
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Pythagorean theorem - a squared plus b squared equals c squared. g g g g g g g g g g
the hypotenuse is always c.
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Proving right triangles congruent - hypotenuse leg.
g g g g g g
Right triangle ratios -
g g g g
Slope - from left to right. up the hill is positive slope. down the hill is negative slope. a
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horizontal line has 0 slope and a verical line as an undefined slope.
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Point slope form of a line - y minus y one equals slope (m) times x minus x one.
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Slope intercept form of a line - y equals slope (m) times x plus the y intercept (b)
g g g g g g g g g g g g g g g g g
Slope formula - y two minus y one divided by x two minus x one.
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rise over run.
g g
correct answers
g g
Tangent - intersects a circle in only 1 place.
g g g g g g g g
Secant - intersects a circle in 2 places.
g g g g g g g
Intersection of a tangent and a radius - form right angles when they intersect.
g g g g g g g g g g g g g
Equation of a circle - x minus h squared plus y minus k squared equals radius squared.
g g g g g g g g g g g g g g g g
Circumference of a circle - 2 times pi times radius or pi times diameter.
g g g g g g g g g g g g g
Area of a circle - pi times radius squared.
g g g g g g g g
Central angle - is equal to its intercepted arc.
g g g g g g g g
Inscribed angle - is equal to ½ its intercepted arc.
g g g g g g g g g
Angle formed by 2 chords intersecting in a circle - is equal to the sum of the arcs
g g g g g g g g g g g g g g g g g
divided by 2.
g g g
Angle formed by 2 secants - is equal to the major arc minus the minor arc divided by 2.
g g g g g g g g g g g g g g g g g g
Angle formed by a secant and a tangent - is equal to the major arc minus the minor arc
g g g g g g g g g g g g g g g g g g
divided by 2.
g g g
Angle formed by two tangents - is equal to the major arc minus the minor arc divided by
g g g g g g g g g g g g g g g g g
2.
g
Lengths of 2 intersecting chords - part of the first chord times the other part of the first
g g g g g g g g g g g g g g g g g
chord equals a part of the second chord times the other part of the second chord.
g g g g g g g g g g g g g g g g
Lengths of an intersecting diameter and chord that meet at right angles (perpendicular) -
g g g g g g g g g g g g g
if a diameter meets a chord at a right angle (perpendicular), the diameter divides the
g g g g g g g g g g g g g g g
chord into 2 equal parts.
g g g g g
Lengths of 2 intersecting secants - the whole length of the first secant times the outside
g g g g g g g g g g g g g g g
length of the first secant equals the whole length of the second secant times the outside
g g g g g g g g g g g g g g g g
length of the second secant.
g g g g g
,Lengths of an instersecting secant and tangent - the whole length of the first secant
g g g g g g g g g g g g g g
times the outside length of the first secant equals the length of the tangent squared.
g g g g g g g g g g g g g g g
Lengths of intersecting tangents - Tangents to a circle sharing a common vertex are
g g g g g g g g g g g g g
equal.
g
Angles - acute angles are less than 90 degrees. Right angles are 90 degrees. obtuse
g g g g g g g g g g g g g g
angles are between 90 and 180 degrees. Straight angles are 180 degrees and reflex
g g g g g g g g g g g g g g
angles are greater than 180 degrees.
g g g g g g
Adjacent angles - share a common vertex, a common side, but not common interior
g g g g g g g g g g g g g
points.
g
Complementary angles - 2 angles when added together that equal 90 degrees.
g g g g g g g g g g g
They do not have to be adjacent angles.
g g g g g g g
Supplementary angles - 2 angles when added together that equal 180 degrees.They do
g g g g g g g g g g g g
not have to be adjacent angles.
g g g g g g
Vertical angles - vertical angles are congruent.
g g g g g g
Alternate interior angles - alternate interior angles are congruent.
g g g g g g g g
Corresponding angles - corresponding angles are congruent. g g g g g g
Sum of the angles in a triangle - the 3 angles of a triangle add up to 180 degrees.
g g g g g g g g g g g g g g g g g g
Triangles classified by sides - scalene triangles have no equal sides.
g g g g g g g g g g
isosceles triangles have at least 2 equal sides.
g g g g g g g
equilateral triangles have 3 equal sides. g g g g g
Triangles classified by angles - acute triangles have 3 acute angles.
g g g g g g g g g g
right triangles have a 90 degree and 2 acute angles.
g g g g g g g g g
obtuse triangles have an obtuse and 2 acute angles.
g g g g g g g g
Exterior angle of a triangle - the exterior angle of a triangle equals the sum of the 2
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opposite interior angles.
g g g
Isosceles triangles - sides opposite congruent angles are congruent.
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angles opposite congruent sides are congruent.
g g g g g
Triangle inequality theorem - the sum of 2 sides of a triangle must be greater than the
g g g g g g g g g g g g g g g g
3rd side.
g g
, Mid segment of a triangle - a mid segment connects the midpoint of 2 sides of a triangle
g g g g g g g g g g g g g g g g g
and is equal to ½ the side not containing the 2 midpoints.
g g g g g g g g g g g g
Median - bisects the opposite side into 2 congruent line segments.
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they meet in a triangle at a point called the centroid.
g g g g g g g g g g
median segments are in a ratio of 2 to 1.
g g g g g g g g g
Angle bisector - bisects an angle into 2 congruent angles.
g g g g g g g g g
they meet in a triangle at a point called the incenter.
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Altitude - makes a right angle with the opposite side.
g g g g g g g g g
they meet in a triangle at a point called the orthocenter.
g g g g g g g g g g
Perpendicular bisector - bisects and makes a right angle with a side of a triangle.They
g g g g g g g g g g g g g g
meet in a triangle at a point called the circumcenter.
g g g g g g g g g g
Similar triangles - angles in similar (∼) triangles are congruent.
g g g g g g g g g
sides are in proportion.
g g g
angles are in a proportion of one to one. (1:1)
g g g g g g g g g
Proving triangles similar - need only 2 angles to be congruent to probe 2 triangles
g g g g g g g g g g g g g g
similar.
g
Proving triangles congruent - can not be angle angle side (A.S.S.) or side side
g g g g g g g g g g g g g
angle(S.S.A.).
g
C.P.C.T.C. - corresponding parts of congruent triangles are congruent.
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Pythagorean theorem - a squared plus b squared equals c squared. g g g g g g g g g g
the hypotenuse is always c.
g g g g
Proving right triangles congruent - hypotenuse leg.
g g g g g g
Right triangle ratios -
g g g g
Slope - from left to right. up the hill is positive slope. down the hill is negative slope. a
g g g g g g g g g g g g g g g g g g
horizontal line has 0 slope and a verical line as an undefined slope.
g g g g g g g g g g g g g
Point slope form of a line - y minus y one equals slope (m) times x minus x one.
g g g g g g g g g g g g g g g g g g
Slope intercept form of a line - y equals slope (m) times x plus the y intercept (b)
g g g g g g g g g g g g g g g g g
Slope formula - y two minus y one divided by x two minus x one.
g g g g g g g g g g g g g g
rise over run.
g g
