Differences between Similar Triangle and Special Triangle

Similar triangles are triangles with the same shape but different sizes. Similar items include all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, their respective angles are congruent and their corresponding sides are proportionate. Due to the links between their angles and ratios, special triangles make calculating a missing side easy.

Special Triangle

Although all right triangles have unique characteristics, some have characteristics that make calculating the length of a missing side without the Pythagorean theorem or trigonometric functions easier. This is why they’re referred to as “special triangles.”

A right triangle is defined as a triangle having one 90° angle. The hypotenuse is always the longest side and is always on the opposite side of the 90° angle. The legs on the opposite two sides may or may not be the same length.

The Pythagorean Theorem is useful for determining the third side of a right triangle when two other sides are known. Some triangles, such as the 30°-60°-90° degree and45°-45°-90°degree triangles are sufficiently common that knowing the side ratios without using the Pythagorean Theorem each time is useful. When you only know one side length, you can use these patterns to completely solve for the missing sides of these particular triangles.

Pythagorean Triple Triangles

Special right triangles with integer sides are known as Pythagorean number triples. While the angles are not integers, the side ratios are extremely useful because they appear in so many places. Knowing these number triples also helps you save time by avoiding having to repeat the Pythagorean Theorem.

Special Right Triangles

The most commonly identified angles with a circle are the central angles, however they are far from the only ones. Angles can be drawn in the circle’s perimeter or created by intersecting chords and other lines.

Right isosceles triangle: The isosceles right triangle possesses both isosceles and right triangle characteristics. Two sides are equal, two angles are equal, and one angle is right.

Similar Triangle

Similar triangles have corresponding sides that are proportional to each other and corresponding angles that are equal. Although similar triangles appear to be the same, their diameters might vary. In general, comparable triangles are different from congruent triangles. There are several methods for determining if two triangles are similar or not. Similar triangles are triangles that have a similar appearance but differ in size. When two objects have the same shape but differ in size, they are considered to be comparable. Similar shapes superimpose each other when amplified or demagnified. “Similarity” refers to the property of comparable shapes.

Similar Triangles Examples

Triangles with comparable angle pairs that are equal are known as similar triangles. Equiangular triangles are comparable in this way. As a result, all equilateral triangles might be considered comparable triangles. Similar triangles are triangles that are different from congruent triangles.

Special about similar triangles

Similar triangles are triangles with the same shape but different sizes. Similar items include all equilateral triangles and squares with any side length. To put it another way, if two triangles are comparable, their respective angles are congruent and their corresponding sides are proportionate.

Similar Triangles Theorems

The similarity theorems can be used to determine or prove whether two triangles are similar. When we don’t have the length of all the triangle’s sides or the length of all its angles, we apply these similarity criteria. These theorems about comparable triangles allow us to rapidly determine if two triangles are similar or not. There have been three major types of similarity rules, as mentioned below,

Angle-Angle Similarity Theorem (AA OR AAA)

Theorem of Side-Angle-Side Similarity (SAS)

Theorem of Side-Side-Side Similarity (SSS)

Differences Between Similar Triangle and Special Triangle

Conclusion

In mathematics, we say that two things are comparable if they have the same shape, but not necessarily the same size. This means we can get one figure from the other by expanding or contracting it, followed quickly by translation, rotation, or reflection. It has congruent if the objects are also have  the identical size.

To prove that two triangles are comparable, we use the methods SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle), AAS (angle-angle-side), and AAA(angle-angle-angle). It’s worth noting that, in contrast to congruent figures, side here refers to the same ratio of side lengths. Also, because the total of angles in a triangle is equal to 180 degree the method AAA is comparable to AA.