No.
Alternate Interior Angles
true
The centroid, circumcenter and orthocenter are the 3 points of concurrency that always lie on a line.
SOMETIMES. I just did that problem in my California geometry book. They can either be parallel or skew...making the answer sometimes.
Well honey, a 27-sided polygon has 27 interior angles. To find the sum of those angles, you use the formula (n-2) * 180, where n is the number of sides. So, for a 27-sided polygon, you'd have (27-2) * 180 = 4,860 degrees. Math doesn't lie, darling.
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.
sides
It must be an obtuse angled triangle.
No.
The orthocenter of a triangle may lie outside the triangle since the ___altitude___ may not intersect any side of the triangle. * * * * * No. One of the altitudes must intersect the side opposite it and so it is not correct to say ANY side of the triangle.
The intersection of the three altitudes of a triangle is called the orthocenter. This point can lie inside the triangle for acute triangles, on the triangle for right triangles, and outside the triangle for obtuse triangles. The orthocenter is one of the triangle's key points of concurrency, along with the centroid and circumcenter.
The interior angles of a triangle must lie within the range (0, 180) degrees. For all other polygons, the interior angles must be in the range (0, 360) excluding 180 degrees.
All three medians MUST lie inside the triangle.
Not normally
The complement of the triangle in the plane.
Those are "alternate interior" angles. They're always equal.
The circumcenter of a triangle will lie inside the triangle if the triangle is acute, meaning all its angles are less than 90 degrees. In this case, the perpendicular bisectors of the triangle's sides intersect at a point that is located within the triangle. Conversely, if the triangle is obtuse (one angle greater than 90 degrees), the circumcenter will lie outside the triangle. For right triangles, the circumcenter lies at the midpoint of the hypotenuse.