1.5 Geometry Equations
Set up  an equation to solve for x.
 3x = 27
 3x = 30
 3x + 27 + 30 = 180
3x
30
27
If two angles of a ▲ are congruent,
their opposite sides are congruent.
3x
x =
 3x = 27
27
Set up an equation to solve for x.
3x
 3x = 120
 3x + 120 = 180
 3x +  3x + 120 = 180
120
All ∆s have angles that  add up to 180 degrees.
3x
 3x +  3x + 120 = 180
6x +  120 = 180
120
6x = 60
x =
3x
fill
in
the
3rd
angle
Set up an equation to solve for x.
6x
30
 6x = 30
 6x = 54
 6x + 54 = 180
120
54
30
If two angles of a ▲ are congruent,
their opposite sides are congruent.
6x
30
 6x = 54
x =
30
54
Set up an equation to solve for x.
 4x = 100
 4x = 80
 4x + 60 + 100 + 80 = 360
80
100
4x
60
Quadrilateral angles add up to 360 degrees.
 4x + 60 + 100 + 80 = 360
80
100
4x + 240 = 360
4x = 120
x =
4x
60
A
ABC = 120
B
2x
Set up an equation to solve for x
x
 2x + x = 120
 2x  = 120
 2x + x = 180
D
C
A
B
2x
120
x
 2x + x = 120
3x = 120
x =
D
C
ABC = 120
Segment DE is the
midsegment of ∆ABC
Set up an
equation for x
B
4x
D
32
20
A
4x = 18
4x = 20
4x + 20 = 32
18
E
C
D is the midpoint
of segment AB

(the endpoints
      of
midsegments
     are
midpoints)
Segment DE is the
midsegment of ∆ABC
B
4x
D
20
A
4x = 20
x =
Segment DE is the
midsegment of ∆ABC
Set up an
equation
to solve
for x
B
D
32
20
2x + 6
A
18
 2x +6 = 16
 2x +6 = 20
 2x +6 = 32
E
C
Segment DE is the
midsegment of ∆ABC
The midsegment
is half the
length of the
parallel ∆ side
B
D
32
20
2x + 6
A
18
E
2x + 6 = 16
C
x =
2x = 10
Set up an equation
to find x
10x
30
 10x = 5y
 10x = 19
 10x = 30
19
5y
(10x does = 5y, but that equation has two variables)
(move the decimal to solve)
Rectangle diagonals bisect each other.
10x
19
x =
 10x = 19
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