name all the properties to a equilateral traingle and a obtuse triangle
To name all the properties of an equilateral triangle:
1. All three sides of an equilateral triangle are of equal length.
2. All three angles are also of equal measure, and each angle measures 60 degrees.
3. The sum of the measures of the interior angles of an equilateral triangle is always 180 degrees.
4. The altitude (perpendicular line segment) from any vertex of an equilateral triangle intersects the opposite side at its midpoint.
5. The centroid (point of concurrency of the medians) of an equilateral triangle is the same as its orthocenter, circumcenter, and incenter.
6. The circumradius (radius of the circumscribed circle) of an equilateral triangle is equal to one-third of the length of any side.
7. The inradius (radius of the inscribed circle) of an equilateral triangle is equal to one-sixth of the length of any side.
To name all the properties of an obtuse triangle:
1. An obtuse triangle is a triangle with one angle measuring more than 90 degrees.
2. The other two angles in an obtuse triangle must be acute (measuring less than 90 degrees).
3. The sum of the measures of the interior angles of an obtuse triangle is always 180 degrees.
4. The largest angle (the obtuse angle) is opposite the longest side, while the other two sides are smaller in length.
5. An obtuse triangle can have an altitude (perpendicular line segment) drawn from any vertex to the opposite side.
6. The circumcenter (point of concurrency of the perpendicular bisectors of the sides) of an obtuse triangle lies outside the triangle.
7. The centroid (point of concurrency of the medians) and orthocenter (point of concurrency of the altitudes) of an obtuse triangle can also lie outside the triangle.