Download Triangles to Order

ANSWER KEY
Student Name: ____________________________________________________
Triangles to Order
Zero, One, Two, Many Handout
4
Instructions
Tell whether you can make 0, 1, 2, or many triangles to meet each set of specifications. If 1, make the triangle.
If 2, make both of them. If many, make 3 different triangles that fit all the conditions. And if 0, explain why it’s
impossible to make such a triangle (a diagram can help!).
1.
One triangle
(ASA).
C
AC
2.
BC
45 º
A
AB
90 º
One triangle
(SAS).
C
4 cm BC
AC
B
60 º
A
2 cm
3.
AB
3 cm
C
30°
B
4.
C
3 cm BC
AC
A
AC
B
30 º
AB
One triangle
(Hypotenuse-leg;
angle C is 90°).
BC
90° 30º
A
6 cm
AB
5.
B
5 cm
6.
C
3 cm BC
AC
A
B
15º
AB
6 cm
C
75°
Two triangles (SSA). If you
make side AB (6 cm) and
angle A (15°), you now have
to figure out side BC (3 cm).
Imagine it swinging from point
B. It can rest its end on the
line coming out of A in two
places, marked C1 and C2.
Either of these could be the
third vertex of the triangle. 7.
C
AC
A
One triangle
(Two angles give
a third—60°—
and you have
ASA. This result
is similar to #3).
BC
120º
90º
No triangles.
Sum of angles
is too great.
B
6 cm
AB
8.
AC
A
BC
60°
45°
Many triangles, all
similar (Sum of
angles is 180°).
B
C
AC
2 cm
2014 http://math.serpmedia.org/diagnostic_teaching/
BC
B
A
AB
AB
2 cm
5 cm
No triangles,
because of the
triangle
inequality: the
two 2-cm
sides are not
long enough to
meet opposite
the 5-cm side.