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Geometry – Quarterly #3 Test – Formula Sheet
Coordinate Geometry:
Distance Formula: d = √(π‘₯2 βˆ’ π‘₯1 )2 + (𝑦2 βˆ’ 𝑦1 )2
π‘₯1 +π‘₯2 𝑦1 +𝑦2
Midpoint: (
2
,
2
)
Right Triangle Formulas:
Pythagorean Theorem:
If a right triangle has legs with measures a and b
and hypotenuse with measure c, then…
c
a
a 2 + b2 = c 2
b
Converse of Pythagorean Theorem:
c 2 > a 2 + b2
obtuse βˆ†
c 2 = a 2 + b2
right βˆ†
c 2 < a 2 + b2
acute βˆ†
Trigonometric Ratios:
sin A =
hypotenuse
opposite
cos A =
adjacent
A
𝑙𝑒𝑔 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
𝑙𝑒𝑔 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
𝑙𝑒𝑔 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
tan A = 𝑙𝑒𝑔 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
Special Right Triangles:
hypotenuse = leg ● √2
hypotenuse = 2 ● shorter leg
longer leg = shorter leg ● √3
Midsegments:
Triangle:
midsegment
1
midsegment = ● base
2
OR
2 ● midsegment = base
base
Trapezoid:
π‘π‘Žπ‘ π‘’1
1
midsegment = (π‘π‘Žπ‘ π‘’1 + π‘π‘Žπ‘ π‘’2 )
2
OR
2 ● midsegment = π‘π‘Žπ‘ π‘’1 + π‘π‘Žπ‘ π‘’2
midsegment
π‘π‘Žπ‘ π‘’2
Polygons:
Sum of interior angle measures = (n – 2)180°
Measure of each interior angle of a regular polygon =
Measure of each exterior angle of a regular polygon =
(π‘›βˆ’2)180°
where n is the
number of sides
𝑛
360°
𝑛
Plane Figure Formulas:
P = 2l + 2w
P = 4s
l
A = s2
s
A = lw
w
a
c
P=a+b+c
h
A=
b
1
2
bh
●
r
C = 2πœ‹r
A = πœ‹r2
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