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Similar Triangles Calculator

Check whether two triangles are similar or find the missing length of a triangle with the help of this similar triangles calculator.

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Use the similar triangles calculator to check the similarity of two triangles. With it, you can also find the missing length of a triangle.

What Are Similar Triangles?

These are the triangles that have the same shape but different sizes. Meanwhile, similar triangles superimpose each other when they are magnified or demagnified. These triangles are different from congruent triangles. The similarity of triangles is denoted by the ‘~’ symbol.

Similar Triangles Formula:

Two triangles △ABC and △EFG can be said to be similar triangles (△ABC ∼ △EFG) if:

∠A = ∠E, ∠B = ∠F and ∠C = ∠G

AB/EF = BC/FG = AC/EG

Similar Triangles and Congruent Triangles:

 Similar Triangles Congruent Triangles They have the same shape but different size They have the same shape and size The symbol is ‘~’ The symbol is ‘≅’ all the corresponding sides  have the same Ratio The ratio of corresponding sides is equal to a constant

What are Three Similarities Theorems For Triangles?

Similarity theorems help to prove whether two triangles are similar or not. These theorems are used when all the sides or angles are not given. Three similarity theorems are:

AA (or AAA) or Angle-Angle:

This theorem states that if the two angles of a triangle are equal to the two angles of another triangle then they are similar triangles.

SAS or Side-Angle-Side:

If the two sides of a given triangle are in proportion to the two sides of another triangle and the angles associated with these sides of both triangles are equal then they are similar triangles.

SSS or Side-Side-Side:

If all the corresponding ratios of all the sides of both triangles are equal then it means that they are similar triangles.

How To Find Similar Triangles?

Go through the following steps to determine whether two triangles are similar or not:

• First of all, note down the given dimensions including the sides or angles of the triangles on paper
• See if these dimensions follow any of the above-mentioned conditions of similar triangles theorems(AA, SSS, SAS)
• If the dimensions of these triangles fulfill any of the conditions then represent them with the ‘~’ symbol

Using an online similar triangles calculator is the most convenient way to determine the similarity of the triangles. Just add the available dimensions and get to

Example:

Suppose you have two triangles if △ABC and △PQR that are similar triangles or not using the given data: ∠A = 65°, ∠B = 60º and ∠P = 70°, ∠R = 45°.

Solution:

Given that:

∠A = 65°

∠B = 70º

And

∠P = 70°

∠R = 45°

Now we have to find the third angle of each triangle to conclude: As we know the sum of all the angles is = 180°

First Triangle = 70° + 65º = 135°

Second Triangle = 70° + 45º = 115°

Now the thrid angle of the first triangle = 180° - 135º = 45º

Now the third angle of the second triangle = 180° - 115º = 65º

Here both of the triangles have two same angles so according to the first theorem of similarity and the similar triangles formula these two triangles are similar. If you are not getting the concept, then use a similar triangles calculator. It will let you find out whether the triangles are similar are not by just requiring the dimensions of the triangles.

How Do You Find The Missing Side of a Similar Triangle?

Follow the below-mentioned steps to find the missing side:

• First, determine whether the triangle that has missing sides is smaller or larger
• Calculate the scale factor “k” of the similar triangle by taking the ratio of any known sides
• If the triangle is small then divide the corresponding side in the larger by “k”
• If the triangle is larger, then multiply the corresponding side in the smaller triangle by the value of k

How Does Similar Triangles Calculator Work?

Provide the available sides or the angles to this similar triangle calculator and get to know whether they are similar or not in seconds. Through it, you can also find the missing sides of a triangle. Let's see how it works!

What Do You Need to Enter?

Inputs For Checking Similarity:

• Similarity Criterion: First choose the type of criteria to check the similarity of the triangles according to the available data.
• Input the Triangle Data: Add the lengths of the sides for the triangles or angles in the specified fields.

This is What You Will Get!

• It provides you with a statement defining whether the triangles are similar or not

Inputs For Finding the Missing Sides:

• Corresponding Sides of The Similar Triangle: Add the values of the sides of a similar triangle
• Scale Factor: Calculate the scale factor of the triangle by taking the ratio of the known sides

This is What You Will Get!

• Missing Sides
• Area of The both Triangles
• The perimeter of both Triangles

With the help of this similar figures calculator, you can quickly and easily assess the similarity of two given triangles.

Applications of Similar Right Triangles Calculator:

Let's take a look at the following applications:

• Students can use the triangle similarity calculator to verify their geometry problems. Teachers can use it to explain the concept of similarities
• Graphic designers use similar polygons calculators to achieve precise scaling in images.

Using a similar triangle calculator, allows you to perform the whole calculation in a matter of seconds.

FAQ’s:

Are Similar Triangles And Congruent Triangles The Same?

Similar triangles have the same shape but different sizes, and on the other hand, congruent triangles have the same shape and same size.

Are All Equilateral Triangles Similar?

Yes, all the equilateral triangles have the same features.

How To Find The Proportion of Similar Triangles?

If two similar triangles have sides X, Y, Z and x, y, z then the pair of corresponding sides are proportion:

X : x = Y : y = Z : z

What Are The Properties of Similar Figures?

The properties of similar triangles are:

• Two triangles have the same shape but different sizes
• One pair of corresponding angles is equal
• The ratio of corresponding sides is the same

How Do You Find Similar Right Triangles?

If you have a right triangle in which the lengths of the hypotenuse and the leg of a right triangle are proportional to the parts of another right triangle then they are called similar. For the precise calculation, you should get the assistance of a similarity in right triangles calculator.

References:

Cuemath.com: Similar Triangles. Wikipedia: Similarity system of triangles, Triangles appended to a rectangle, Gallery