two slightly smaller triangles of equal size :)
The medians of a triangle are concurrent and the point of concurrence, the centroid, is one-third of the distance from the opposite side to the vertex along the median
Draw a line from any vertex to a point on one of the adjacent sides and cut along it.
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
Because they represent a pair of coordinates
A rhombus
A 30-60-90 right triangle
The medians of a triangle are concurrent and the point of concurrence, the centroid, is one-third of the distance from the opposite side to the vertex along the median
Draw a line from any vertex to a point on one of the adjacent sides and cut along it.
Suppose you have a triangle whose vertices are A, B and C, and the sides opposite these vertices are a, b and c, respectively. Cut out the triangle. Fold it so that vertex B meets vertex C. Mark the point where this fold is on side a. Mark this point as D and fold along AD. Fold it so that vertex A meets vertex C. Mark the point where this fold is on side b. Mark this point as E and fold along BE. Fold it so that vertex A meets vertex B. Mark the point where this fold is on side c. Mark this point as F and fold along CF. The three folds, AD, BE and CF meet at the circumcentre. You do not need all three - any two of them will do.
Infinitely many. Take two triangles. Let a vertex of triangle A just touch the side of the other triangle, B. Change the angle of triangle A. there are infinitely many angles and so infinitely many orientations for A.Not only that. Slide triangle A along the side of triangle B. There are infinitely many points on the side of B so that's an infinite number of shapes.And that is with just two triangles!Infinitely many. Take two triangles. Let a vertex of triangle A just touch the side of the other triangle, B. Change the angle of triangle A. there are infinitely many angles and so infinitely many orientations for A.Not only that. Slide triangle A along the side of triangle B. There are infinitely many points on the side of B so that's an infinite number of shapes.And that is with just two triangles!Infinitely many. Take two triangles. Let a vertex of triangle A just touch the side of the other triangle, B. Change the angle of triangle A. there are infinitely many angles and so infinitely many orientations for A.Not only that. Slide triangle A along the side of triangle B. There are infinitely many points on the side of B so that's an infinite number of shapes.And that is with just two triangles!Infinitely many. Take two triangles. Let a vertex of triangle A just touch the side of the other triangle, B. Change the angle of triangle A. there are infinitely many angles and so infinitely many orientations for A.Not only that. Slide triangle A along the side of triangle B. There are infinitely many points on the side of B so that's an infinite number of shapes.And that is with just two triangles!
The vertex of a prism is a corner along the side of the prism. There are 8 vertices on a rectangular prism.
There is no such thing as an equator triangle. A triangle with its base along the equator and its other vertex elsewhere can have angles adding up to just over 180 to just under 540 degrees. The nearer to the pole, and the longer the base, the greater the angular sum.
The surface generated by a straight line, the generator, passing through a fixed point, the vertex, and moving along a fixed curve, the directrix.A right circular cone.
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
It depends on what the motion is. If the square is sliding along a straight line then the path of the vertex is a straight line. If the square is rotating, the answer will vary according to the location of the centre of rotation.
Cone ( not including the vertex ) Cylinder ( APEX )
If there is no centre of enlargement then just draw the octagon with each side three times as long.If there is a centre of enlargement:join each vertex to the centre;measure the distance from the centre to the vertex;triple this measurement;plot the vertex at this length along the line from the centre that passes through the vertex;join the vertices of the new octagon which were joined in the original octagon.Step 2 and 3 are easier if done by considering the x and y movements separately; for example if the centre is at (1, 2) and a vertex is at (3, 5), then the distance between the centre and the vertex is (3-1, 5-2) = (2, 3); tripling this gives (2×3, 3×3) = (6, 9), so the corresponding vertex of the new octagon would be at (1+6, 2+9) = (7, 11)