Download TRANSVERSALS Thms

// Lines, ∠ngles, & Tri∆ngles
GEOMETRY
Transversals
(corr. ∠ ‘s)
Name
AIA
Corresponding Angles Def.
are angles in the same relative
locations to the transversal line (i.e.
upper right, lower left, lower right,
upper left etc.)
Picture
Corresponding Angles Postulate/Thm.
ll lines ⇔ ≅ corr. ∠’s
Lines are parallel if and only if
corresponding angles are congruent.
Theorem
ll lines ⇔ ≅ A.I.A.
Alternate Interior Angles are congruent
if and only if
lines are parallel.
Alternate
Interior
Angles
AEA
ll lines ⇔ ≅ A.E.A.
Alternate Exterior Angles are congruent
if and only if
lines are parallel.
Alternate
Exterior
Angles
SSI
Unique
Perpendicular
Line
Through a point
not on a line,
there is exactly
one
perpendicular
line.
ll lines ⇔ S.S.I ∠’s = 180°.
Same-Side Interior Angles are supplementary
if and only if
lines are parallel.
SameSide
Interior
SSE
ll lines ⇔ S.S.E ∠’s = 180°.
Same-Side Exterior Angles are supplementary
if and only if
lines are parallel.
SameSide
Exterior
Perpendicular to Parallels Thm.
⊥ l & l // p ⇒ t ⊥ p
t
Two Perpendiculars Thm.
t
l
If a line is perpendicular to one of two
parallel lines, then it is also
perpendicular to the second line.
TRIANGLE THEOREMS
p
POLYGONS
2
3
Unique
Parallel Line
Through a
point not on a
line, there is
exactly one
parallel line.
1
4
int. ∠
t ⊥ l & t ⊥ p ⇒ l // p
If two lines are perpendicular to the
same line in the same plane, then they
are parallel to each other.
Interior Angle Sum
= 180 (n–2)
Interior Angle Measure
= 180 (n–2)
n
ext. ∠
Triangle Sum Theorem
m∠1 + m∠2 + m∠3 = 180°
Exterior Angle Sum
= 360°
Exterior Angle Theorem
m∠4 = m∠2 + m∠3
Exterior Angle Measure
= 360÷n
Central Angle
= 360°÷n
r
p
l
Parallel Transitivity (3
//’s) Thm.
r // p & p // l
⇒ r // l
If two lines are parallel to
a third line, then they are
parallel to each other.