If the angles are the same and the sides are proportional by ratio then they are said to be similar triangles.
Trigonometric ratios are characteristics of angles, not of lengths. And, by definition, the corresponding angles an similar triangles have the same measures.
You muliply the base times the height of one of the triangles in the trianagular prism (both triangles will be similar, proportional, and equal, and you divide that number by two or multiply that number by 1/2, then you multiply that number times the height or length of one triangle's end to the other triangle's end of the triangular prism to obtain your final volume. The formula is as follows. V=1/2(b*h)(height)
That's the definition of trigonometry. Triangles are completely dependent upon their side lengths, and can be defined by only three values.
Ancient Egyptian and Babylonian mathematicians lacked the concept of an angle measure, but they studied the ratios of the sides of similar triangles and discovered some properties of these ratios. The ancient Nubians used a similar methodology.
The relationship between an angle and the triangle formed by it is always constant. This is also why sin cos and tan obtained from the unit circle can be applied to all triangles with the same angle. All that matters is the ratio of the sides, so the calculator can "pick" any length for one side, and use that and the angle to find the other side(s). This answer will be the same regardless of which triangle you are specifically referring to. Side lengths 3 and 5 will produce the same trig values as sides 21 and 35. Also, given the processing power of most calculators, these values are often programmed in, similar to how many students are "programmed" to know the trig values for major angles such as pi, pi/4, 30deg, and 60deg.
why triangle are similar
Yes, similar triangles are congruent because in order to be congruent they must first be equal. Which in turn is the definition of a similar triangle. A triangle equal in angle measurements and/or side lengths. So, yes.
The triangles are similar.
I honestly don't know much stuff about triangles.
If ll the angles of one triangle are the same as the angles of another triangle they are similar. Rotation is always allowed and mirroring often can be allowed.
No. You can have two triangles that are congruent to one another, and two quadrilaterals that are congruent to one another. But the triangle cannot be similar to the quadrilateral!
Yes they are similar
I think they are similar because a triangle can fit into a circle and vise versa.
Yes.
Triangles that are the same shape but not the same size. In order to be a similar triangle, their numbers have to form proportions with the numbers of the similar triangle.
90 degree triangles are always similar.
if any two angles are similar the triangle will be similar