NYSTCE CST 245 ALL 2026 CORE EXAM TEST QUESTIONS
AND ANSWERS GUARANTEE A+
✔✔Text comprehension - ✔✔the reason for reading: understanding what is read, with
readers reading actively (engaging in the complex process of making sense from text)
and with purpose (for learning, understanding, or enjoyment).
✔✔Vocabulary - ✔✔the words a reader knows. Listening vocabulary refers to the words
a person knows when hearing them in oral speech. Speaking vocabulary refers to the
words we use when we speak. Reading vocabulary refers to the words a person knows
when seeing them in print. Writing vocabulary refers to the words we use in writing.
✔✔Word parts - ✔✔include affixes (prefixes and suffixes), base words, and word roots.
✔✔Word roots - ✔✔words from other languages that are the origin of many English
words. About 60% of all English words have Latin or Greek origins.
✔✔reflexive property - ✔✔a segment or angle is always congruent to itself
✔✔segment bisection - ✔✔a point, segment, ray, or line that divides a segment into 2
congruent segments
✔✔midpoint - ✔✔the point where a segment is bisected; cuts the segment into 2
congruent parts
✔✔segment trisection - ✔✔two points, segments, rays, lines, or any combination
thereof that divide a segent into 3 congruent segments
✔✔angle bisection - ✔✔a ray that cuts an angle into 2 congruent angles
✔✔angle trisection - ✔✔2 rays that divide an angle between 3 congruent angles
✔✔theorem: complements of the same angle are congruent - ✔✔If 2 angles are each
complementary to a 3rd angle then they're congruent to each other.
✔✔theorem: complements of congruent angles are congruent - ✔✔If 2 angles are
complementary to 2 other congruent angles, then they're congruent.
✔✔theorem: supplements of the same angle are congruent - ✔✔If 2 angles are each
supplementary to a 3rd angle, then they're congruent.
✔✔theorem: supplements of congruent angles are congruent - ✔✔If 2 angles are
supplementary to 2 other congruent angles, then they're congruent.
,✔✔theorem: segment addition (3 total segments) - ✔✔If a segment is added to 2
congruent segment, then the sums are congruent
✔✔theorem: angle addition (3 total angles) - ✔✔If an angle is added to two congruent
angles, then the sums are congruent.
✔✔theorem: segment addition (4 total segments) - ✔✔If 2 congruent segments are
added to 2 other congruent segments, then the sums are congruent
✔✔theorem: angle addition (4 total angles) - ✔✔If 2 congruent angles are added to 2
other congruent angles, then the sums are congruent
✔✔theorem: segment subtraction (3 total segments) - ✔✔If a segment is subtracted
from 2 congruent segments, then the differences are congruent.
✔✔theorem: angle subtraction (3 total angles) - ✔✔If an angle is subtracted from 2
congruent angles, then the differences are congruent.
✔✔theorem: segment subtraction (4 total segments) - ✔✔If 2 congruent segments are
subtracted from 2 other congruent segments, then the differences are congruent.
✔✔theorem: angle subtraction (4 total angles) - ✔✔If 2 congruent angles are subtracted
from 2 other congruent angles, then the differences are congruent.
✔✔theorem: like multiples - ✔✔If 2 segments or angles are congruent, then their like
multiples are congruent.
EXAMPLE: If you have 2 congruent angles, then 3 times one angle will equal 3 times
the other angle.
✔✔theorem: like division - ✔✔If 2 segments or angles are congruent, then their like
divisions are congruent.
EXAMPLE: If you have 2 congruent segments, then 1/4 of one segment equals 1/4 of
the other segment.
✔✔postulate: substitution - ✔✔If 2 segments are equal to the same segment, then
they're equal to each other.
✔✔vertical angles - ✔✔When 2 lines intersect to form an "X", angles on the opposite
sides of the "X."
✔✔theorem: vertical angles are congruent - ✔✔If 2 angles are vertical angles, then
they're congruent.
, ✔✔transitive property (for 3 segments/angles) - ✔✔If 2 segments or angles are each
congruent to a 3rd segment or angle, then they're congruent to each other.
EXAMPLE: If ∠ A ≅ ∠ B, and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C
✔✔transitive property (for 4 segments/angles) - ✔✔If 2 segments or angles are
congruent to congruent to congruent segments or angles, then they're congruent to
each other.
EXAMPLE: Segment AB ≅ Segment CD, Segment CD ≅ Segment EF, and Segment
EF ≅ Segment GH, then Segment AB ≅ GH
✔✔substitution property - ✔✔If 2 geometric objects (segments, angles, triangles, etc.)
are congruent an you have a statement involving one of them, you can replace the one
with the other.
EXAMPLE: If ∠X ≅ ∠Y, and ∠Y is supplementary to ∠Z, then ∠X is supplementary to
∠Z.
✔✔triangle inequality principle - ✔✔the sum of the lengths of any 2 sides of a triangle
must be greater than the length of the 3rd side.
✔✔median of a triangle - ✔✔a segment that goes from one of the triangle's vertices to
the midpoint of the opposite side
✔✔centroid - ✔✔where the 3 medians of a triangle intersect; the triangle's balancing
point or center of gravity
✔✔incenter - ✔✔the point of concurrency of the three angle bisectors of a triangle
✔✔circumcenter - ✔✔where the 3 perpendicular bisectors of the sides of a triangle
intersect; the circumcenter is the center of a circle circumscribed about (drawn around)
the triangle
✔✔orthocenter - ✔✔where the triangle's 3 altitudes intersect
✔✔congruent triangles - ✔✔triangles in which all pairs of corresponding sides and
angles are congruent
✔✔theorem: side-side-side (SSS) - ✔✔If 3 sides of one triangle are congruent to 3
sides of another triangle, then the triangles are congruent
✔✔theorem: side-angle-side (SAS) - ✔✔If 2 sides and the included angle of one
triangle are congruent to 2 sides and the included angle of another triangle, then the
triangles are congruent
AND ANSWERS GUARANTEE A+
✔✔Text comprehension - ✔✔the reason for reading: understanding what is read, with
readers reading actively (engaging in the complex process of making sense from text)
and with purpose (for learning, understanding, or enjoyment).
✔✔Vocabulary - ✔✔the words a reader knows. Listening vocabulary refers to the words
a person knows when hearing them in oral speech. Speaking vocabulary refers to the
words we use when we speak. Reading vocabulary refers to the words a person knows
when seeing them in print. Writing vocabulary refers to the words we use in writing.
✔✔Word parts - ✔✔include affixes (prefixes and suffixes), base words, and word roots.
✔✔Word roots - ✔✔words from other languages that are the origin of many English
words. About 60% of all English words have Latin or Greek origins.
✔✔reflexive property - ✔✔a segment or angle is always congruent to itself
✔✔segment bisection - ✔✔a point, segment, ray, or line that divides a segment into 2
congruent segments
✔✔midpoint - ✔✔the point where a segment is bisected; cuts the segment into 2
congruent parts
✔✔segment trisection - ✔✔two points, segments, rays, lines, or any combination
thereof that divide a segent into 3 congruent segments
✔✔angle bisection - ✔✔a ray that cuts an angle into 2 congruent angles
✔✔angle trisection - ✔✔2 rays that divide an angle between 3 congruent angles
✔✔theorem: complements of the same angle are congruent - ✔✔If 2 angles are each
complementary to a 3rd angle then they're congruent to each other.
✔✔theorem: complements of congruent angles are congruent - ✔✔If 2 angles are
complementary to 2 other congruent angles, then they're congruent.
✔✔theorem: supplements of the same angle are congruent - ✔✔If 2 angles are each
supplementary to a 3rd angle, then they're congruent.
✔✔theorem: supplements of congruent angles are congruent - ✔✔If 2 angles are
supplementary to 2 other congruent angles, then they're congruent.
,✔✔theorem: segment addition (3 total segments) - ✔✔If a segment is added to 2
congruent segment, then the sums are congruent
✔✔theorem: angle addition (3 total angles) - ✔✔If an angle is added to two congruent
angles, then the sums are congruent.
✔✔theorem: segment addition (4 total segments) - ✔✔If 2 congruent segments are
added to 2 other congruent segments, then the sums are congruent
✔✔theorem: angle addition (4 total angles) - ✔✔If 2 congruent angles are added to 2
other congruent angles, then the sums are congruent
✔✔theorem: segment subtraction (3 total segments) - ✔✔If a segment is subtracted
from 2 congruent segments, then the differences are congruent.
✔✔theorem: angle subtraction (3 total angles) - ✔✔If an angle is subtracted from 2
congruent angles, then the differences are congruent.
✔✔theorem: segment subtraction (4 total segments) - ✔✔If 2 congruent segments are
subtracted from 2 other congruent segments, then the differences are congruent.
✔✔theorem: angle subtraction (4 total angles) - ✔✔If 2 congruent angles are subtracted
from 2 other congruent angles, then the differences are congruent.
✔✔theorem: like multiples - ✔✔If 2 segments or angles are congruent, then their like
multiples are congruent.
EXAMPLE: If you have 2 congruent angles, then 3 times one angle will equal 3 times
the other angle.
✔✔theorem: like division - ✔✔If 2 segments or angles are congruent, then their like
divisions are congruent.
EXAMPLE: If you have 2 congruent segments, then 1/4 of one segment equals 1/4 of
the other segment.
✔✔postulate: substitution - ✔✔If 2 segments are equal to the same segment, then
they're equal to each other.
✔✔vertical angles - ✔✔When 2 lines intersect to form an "X", angles on the opposite
sides of the "X."
✔✔theorem: vertical angles are congruent - ✔✔If 2 angles are vertical angles, then
they're congruent.
, ✔✔transitive property (for 3 segments/angles) - ✔✔If 2 segments or angles are each
congruent to a 3rd segment or angle, then they're congruent to each other.
EXAMPLE: If ∠ A ≅ ∠ B, and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C
✔✔transitive property (for 4 segments/angles) - ✔✔If 2 segments or angles are
congruent to congruent to congruent segments or angles, then they're congruent to
each other.
EXAMPLE: Segment AB ≅ Segment CD, Segment CD ≅ Segment EF, and Segment
EF ≅ Segment GH, then Segment AB ≅ GH
✔✔substitution property - ✔✔If 2 geometric objects (segments, angles, triangles, etc.)
are congruent an you have a statement involving one of them, you can replace the one
with the other.
EXAMPLE: If ∠X ≅ ∠Y, and ∠Y is supplementary to ∠Z, then ∠X is supplementary to
∠Z.
✔✔triangle inequality principle - ✔✔the sum of the lengths of any 2 sides of a triangle
must be greater than the length of the 3rd side.
✔✔median of a triangle - ✔✔a segment that goes from one of the triangle's vertices to
the midpoint of the opposite side
✔✔centroid - ✔✔where the 3 medians of a triangle intersect; the triangle's balancing
point or center of gravity
✔✔incenter - ✔✔the point of concurrency of the three angle bisectors of a triangle
✔✔circumcenter - ✔✔where the 3 perpendicular bisectors of the sides of a triangle
intersect; the circumcenter is the center of a circle circumscribed about (drawn around)
the triangle
✔✔orthocenter - ✔✔where the triangle's 3 altitudes intersect
✔✔congruent triangles - ✔✔triangles in which all pairs of corresponding sides and
angles are congruent
✔✔theorem: side-side-side (SSS) - ✔✔If 3 sides of one triangle are congruent to 3
sides of another triangle, then the triangles are congruent
✔✔theorem: side-angle-side (SAS) - ✔✔If 2 sides and the included angle of one
triangle are congruent to 2 sides and the included angle of another triangle, then the
triangles are congruent
