Download Acceptable Shortened Forms

Geometry
Acceptable Shortened Forms
Theorems
Conditional Form
Shortened Form
If two angles are right angles, then they are congruent.
right ∠s ⇒ ≅
If two angles are straight angles, then they are congruent.
st. ∠s ⇒ ≅
If two angles form a linear pair, then they are supplementary.
linear pair ⇒ supp
If angles are supplementary to the same angle, then they
are congruent.
supps of same ∠ ⇒ ≅
If angles are supplementary to congruent angles, then they
are congruent.
supps of ≅ ∠s ⇒ ≅
If angles are complementary to the same angle, then they
are congruent.
comps of same ∠ ⇒ ≅
If angles are complementary to congruent angles, then they
are congruent.
comps of ≅ ∠s ⇒ ≅
If the same segment/angle is added to congruent
segments/angles, then the sums are congruent.
Addition Prop. of ≅
If congruent segments/angles are added to congruent
segments/angles, then the sums are congruent.
Addition Prop. of ≅
**Similarly, you may use Subtraction Prop of ≅
Subtraction Prop. of ≅
If segments/angles are congruent, then their like multiples
are congruent.
Like multiples ≅
If segments/angles are congruent, then their like divisions
are congruent.
Like divisions ≅
If two angles are vertical angles, then they are congruent.
(No “def. of vertical angles” step required)
Vertical ∠s ⇒ ≅
If angles/segments are congruent to the same or congruent
angles/segments, then they are congruent.
Transitive Prop of ≅
If angles/segments are congruent, then one may replace
the other.
Substitution Prop. of ≅
If two angles are supplementary and congruent, then
they are right angles.
supp + ≅ ⇒ rt ∠s
Definitions
Shortened Form
A right angle is an angle whose measure is 90°
rt. ∠ ⇒ 90°
Congruent segments/angles have equal measures.
≅ ⇒ = meas.
A midpoint divides a segment into two congruent
segments.
mdpt. ⇒ 2 ≅ segs
A segment/angle bisector divides a segment/angle into
two congruent segments/angles.
bis ⇒ 2 ≅ segs/∠s
Complementary angles are two angles whose sum is
a right angle (90°).
comp ⇒ rt ∠
Supplementary angles are two angles whose sum is
a straight angle (180°).
supp ⇒ st ∠
Perpendicular lines, rays, segments meet to form
⊥ ⇒ rt ∠s
An altitude of a triangle is a line segment drawn from
any vertex of the triangle to the opposite side, extended
if necessary, and perpendicular to that side. (An altitude
of a triangle forms right [90°] angles with one of the sides.)
alt ⇒ ⊥ or alt ⇒ rt ∠
A median of a triangle is a line segment drawn from
any vertex of the triangle to the midpoint of the opposite side.
(A median of a triangle divides into two congruent segments,
or bisects the side to which it is drawn.)
med ⇒ mdpt or med ⇒ 2 ≅ segs
A scalene triangle is a triangle in which no two sides are
congruent.
scalene Δ ⇒ no sides ≅
An isosceles triangle is a triangle in which at least two sides
are congruent.
isos Δ ⇒ legs ≅
An equilateral triangle is a triangle in which all sides are
congruent.
equilateral Δ ⇒ all sides ≅
An acute triangle is a triangle in which all angles are
acute.
acute Δ ⇒ all ∠s acute
An obtuse triangle is a triangle in which one angle is
obtuse.
obtuse Δ ⇒ obtuse ∠
A right triangle is a triangle in which one angle is right.
congruent.
right Δ ⇒ rt ∠
or alt ⇒ 90° ∠
or med ⇒ bisect