Similar Triangles

What are Similar Triangles Class 10?

Similar triangles are the triangles which gave all the angles equal and their sides are in a common ratio. They have a similar shape but not a similar area.

What are Similar Triangles Formulas?

Similar triangle formulas are the formulas that tell us whether two triangles are similar or not. For two triangles △ABC and △XYZ, the similar triangles formula are,

• ∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z
• AB/XY = BC/YZ = CA/ZX

Which Symbol is used for representing Similar Triangles?

Similar Triangles are represented using the ‘~’ symbol. If two triangles △ABC and △XYZ are similar we represent them as, △ABC ~ △XYZ, it is read as triangle ABC similar to triangle XYZ.

What are 3 Similar Triangle Theorems?

We can easily prove two triangles to be similar by using three triangle theorem that are,

• AA (or AAA) or Angle-Angle Similarity Theorem
• SAS or Side-Angle-Side Similarity Theorem
• SSS or Side-Side-Side Similarity Theorem

What are Properties of Similar Triangles?

The important properties of the similar triangle are,

• Similar triangles have fixed shapes but their sizes may be different.
• Corresponding angles are equal in a similar triangle.
• Corresponding sides are in common ratios in a similar triangle.

How to know if two Triangles are Similar?

If all the angles in a triangle are equal then we can easily say that triangles are similar.

Which Triangles are always Similar?

The triangle which is always similar is an equilateral triangle. As all the angles in the equilateral triangles are always 60 degrees any two equilateral triangles are always similar.

What is Similar Triangles Area?

The ratio of the area of two similar triangles is always equal to the ratio of squares of their sides. For two triangles △ABC and △XYZ, we can say that,

• area △ABC / area △XYZ = (AB / XY)²

What is Similar Triangle Criteria?

Similar Triangle Criteria is the criteria in which we can declare three triangles as similar triangles and these three criteria are,

• AAA Criteria (Angle-Angle-Criteria)
• SAS Criteria (Side-Angle-Side Criteria)
• SSS Criteria (Side-Side-Side Criteria)

Who is the father of similar triangles?

Euclid, the ancient Greek mathematician often referred to as the “father of geometry,” provided foundational principles for understanding similar triangles in his work “Elements.”

Are similar triangles proportional?

Yes, similar triangles are proportional. This means that the corresponding sides of similar triangles are in proportion, which implies that the ratio of corresponding sides of similar triangles remains constant.

Which triangles are always similar?

Triangles that have the same three angles are always similar. This is a fundamental property known as the Angle-Angle (AA) similarity criterion.

Are all right triangles similar?

No, not all right triangles are similar. While right triangles with the same acute angles are similar, the length of the hypotenuse and the ratio of side lengths may differ, leading to non-similarity between right triangles.

What is the ratio of two similar triangles?

The ratio of any two corresponding sides in similar triangles remains constant. This means that if you take corresponding sides of similar triangles and form a ratio, the result will always be the same, regardless of the specific side lengths chosen.

Similar Triangles are triangles with the same shape but can have variable sizes. Similar triangles have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles are different from congruent triangles. Two congruent figures are always similar, but two similar figures need not be congruent.

Two triangles are considered similar when their corresponding angles match and their sides are proportional. This means that similar triangles have the same shape, although their sizes may differ. On the other hand, triangles are defined as congruent when they not only share the same shape but also have corresponding sides that are identical in length.

Now, let’s learn more about similar triangles and their properties with solved examples and others in detail in this article.