NCSSM PLACEMENT TEST EXAM NEWEST 2025 COMPLETE QUESTIONS
AND CORRECT DETAILED SOLUTIONS (VERIFIED SOLUTIONS )|ALREADY
GRADED A+||BRAND NEW VERSION!!
Isosceles triangles - SOLUTION-sides opposite congruent angles are congruent. angles opposite
congruent sides are congruent.
Triangle inequality theorem - SOLUTION-the sum of 2 sides of a triangle must be greater than the
3rd side.
Mid segment of a triangle - SOLUTION-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 - SOLUTION-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 - SOLUTION-bisects an angle into 2 congruent angles. they meet in
a triangle at a point called the incenter.
Altitude - SOLUTION-makes a right angle with the opposite side. they meet in
a triangle at a point called the orthocenter.
,Perpendicular bisector - SOLUTION-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 - SOLUTION-angles in similar ( ) triangles are congruent. sides are in
proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - SOLUTION-need only 2 angles to be congruent to probe 2 triangles
similar.
Proving triangles congruent - SOLUTION-can not be angle angle side (A.S.S.) or side side
angle(S.S.A.).
C.P.C.T.C. - SOLUTION-corresponding parts of congruent triangles are congruent.
Tangent - SOLUTION-intersects a circle in only 1 place.
Secant - SOLUTION-intersects a circle in 2 places.
Intersection of a tangent and a radius - SOLUTION-form right angles when they intersect.
Equation of a circle - SOLUTION-x minus h squared plus y minus k squared equals radius
squared.
Circumference of a circle - SOLUTION-2 times pi times radius or pi times diameter.
,Area of a circle - SOLUTION-pi times radius squared.
Central angle - SOLUTION-is equal to its intercepted arc.
Inscribed angle - SOLUTION-is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle - SOLUTION-is equal to the sum of the arcs
divided by 2.
Angle formed by 2 secants - SOLUTION-is equal to the major arc minus the minor arc divided by
2.
Angle formed by a secant and a tangent - SOLUTION-is equal to the major arc minus the minor
arc divided by 2.
Angle formed by two tangents - SOLUTION-is equal to the major arc minus the minor arc divided
by 2.
Lengths of 2 intersecting chords - SOLUTION-part of the first chord times the other part of the
first chord equals a part of the second chord times the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles (perpendicular) -
SOLUTION-if a diameter meets a chord at a right angle (perpendicular), the diameter divides the
chord into 2 equal parts.
, Lengths of 2 intersecting secants - SOLUTION-the whole length of the first secant times the
outside length of the first secant equals the whole length of the second secant times the outside
length of the second secant.
Lengths of an instersecting secant and tangent - SOLUTION-the whole length of the first secant
times the outside length of the first secant equals the length of the tangent squared.
Lengths of intersecting tangents - SOLUTION-Tangents to a circle sharing a common vertex are
equal.
Angles - SOLUTION-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 - SOLUTION-share a common vertex, a common side, but not common interior
points.
Complementary angles - SOLUTION-2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles - SOLUTION-2 angles when added together that equal 180 degrees.They
do not have to be adjacent angles.
Vertical angles - SOLUTION-vertical angles are congruent.
Alternate interior angles - SOLUTION-alternate interior angles are congruent.
AND CORRECT DETAILED SOLUTIONS (VERIFIED SOLUTIONS )|ALREADY
GRADED A+||BRAND NEW VERSION!!
Isosceles triangles - SOLUTION-sides opposite congruent angles are congruent. angles opposite
congruent sides are congruent.
Triangle inequality theorem - SOLUTION-the sum of 2 sides of a triangle must be greater than the
3rd side.
Mid segment of a triangle - SOLUTION-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 - SOLUTION-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 - SOLUTION-bisects an angle into 2 congruent angles. they meet in
a triangle at a point called the incenter.
Altitude - SOLUTION-makes a right angle with the opposite side. they meet in
a triangle at a point called the orthocenter.
,Perpendicular bisector - SOLUTION-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 - SOLUTION-angles in similar ( ) triangles are congruent. sides are in
proportion.
angles are in a proportion of one to one. (1:1)
Proving triangles similar - SOLUTION-need only 2 angles to be congruent to probe 2 triangles
similar.
Proving triangles congruent - SOLUTION-can not be angle angle side (A.S.S.) or side side
angle(S.S.A.).
C.P.C.T.C. - SOLUTION-corresponding parts of congruent triangles are congruent.
Tangent - SOLUTION-intersects a circle in only 1 place.
Secant - SOLUTION-intersects a circle in 2 places.
Intersection of a tangent and a radius - SOLUTION-form right angles when they intersect.
Equation of a circle - SOLUTION-x minus h squared plus y minus k squared equals radius
squared.
Circumference of a circle - SOLUTION-2 times pi times radius or pi times diameter.
,Area of a circle - SOLUTION-pi times radius squared.
Central angle - SOLUTION-is equal to its intercepted arc.
Inscribed angle - SOLUTION-is equal to ½ its intercepted arc.
Angle formed by 2 chords intersecting in a circle - SOLUTION-is equal to the sum of the arcs
divided by 2.
Angle formed by 2 secants - SOLUTION-is equal to the major arc minus the minor arc divided by
2.
Angle formed by a secant and a tangent - SOLUTION-is equal to the major arc minus the minor
arc divided by 2.
Angle formed by two tangents - SOLUTION-is equal to the major arc minus the minor arc divided
by 2.
Lengths of 2 intersecting chords - SOLUTION-part of the first chord times the other part of the
first chord equals a part of the second chord times the other part of the second chord.
Lengths of an intersecting diameter and chord that meet at right angles (perpendicular) -
SOLUTION-if a diameter meets a chord at a right angle (perpendicular), the diameter divides the
chord into 2 equal parts.
, Lengths of 2 intersecting secants - SOLUTION-the whole length of the first secant times the
outside length of the first secant equals the whole length of the second secant times the outside
length of the second secant.
Lengths of an instersecting secant and tangent - SOLUTION-the whole length of the first secant
times the outside length of the first secant equals the length of the tangent squared.
Lengths of intersecting tangents - SOLUTION-Tangents to a circle sharing a common vertex are
equal.
Angles - SOLUTION-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 - SOLUTION-share a common vertex, a common side, but not common interior
points.
Complementary angles - SOLUTION-2 angles when added together that equal 90 degrees.
They do not have to be adjacent angles.
Supplementary angles - SOLUTION-2 angles when added together that equal 180 degrees.They
do not have to be adjacent angles.
Vertical angles - SOLUTION-vertical angles are congruent.
Alternate interior angles - SOLUTION-alternate interior angles are congruent.
