If we use mathematical instruments or geometrical software to construct, we have to use similar triangles
to calculate the length of SW first, which is more troublesome.
They cover congruent triangles, similar triangles
, circles and angles, circles and lines, basic facts and techniques in geometry, and geometry problems in competitions.
Mathematical ideas like angle bisection, perpendicular bisector, congruence of shapes and segments, properties of right triangles, similar triangles
, reflection, and rotation become more tangible and vivid in the context of paper folding.
In order to prove this result, we will use similar triangles
shown in the following figure.
For example, all instances of collinear points and all instances of similar triangles
are grouped together.
For example, Cavanagh (2008) encouraged students to use ratio and the principle of similar triangles
to measure the height of the school flagpole.
The cases that do not appear in the list are either cannot occur or lead to similar triangles
Wikipedia's entry about the history of trigonometry is there for all to read (on the website, several reliable sources are referenced at the bottom): "Pre-Hellenic societies such as the ancient Egyptians and Babylonians 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.
In particular, they focused on identifying similar triangles
to determine the length of the height (figure 13).
For example, teachers explain that light travels in a line or that the shadow cast by a person is related by similar triangles
to that cast by a flagpole.
Basic concepts in traditional geometry include similar triangles
and the Pythagorean theorem.
By now a solution idea was bubbling in my brain, based on a memory of working out heights of tall things from shadows and known smaller things, using the idea of similar triangles