5. Match the principal defining characteristics to the proper triangle names:
1. acute triangle
2. scalene triangle
3. isosceles triangle
4. obtuse triangle
5. equilateral triangle
6. right triangle
7. equiangular triangle
a. Side lengths and angles correspond.
b. One angle measures $90^{\circ}$.
c. There is one angle greater than $90^{\circ}$.
d. All sides are a different lengths.
e. All sides are the same length.
f. At least two sides are the same length.
g. All angles are equal in measure.
h. There is no angle greater than $90^{\circ}$.
i. The angles add up to $180^{\circ}$.
Answer
The principal defining characteristic of an acute triangle is \(\boxed{\text{'There is no angle greater than $90^{\circ}$'}}\).
Step 1 ：An acute triangle is a triangle where all angles are less than $90^{\circ}$. So, the characteristic that matches with acute triangle is 'There is no angle greater than $90^{\circ}$'.
Step 2 ：The principal defining characteristic of an acute triangle is \(\boxed{\text{'There is no angle greater than $90^{\circ}$'}}\).
