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If two triangles have the same shape but one is an enlargement of the other they are said to be similar. The two triangles must be equi-angular.

To prove that ∆ABC is similar to ∆XYZ it is necessary to prove one of the following :-

1) Two angles in ∆ABC are equal to two angles in ∆XYZ, since it follows that the third angles will also be equal.

2) The three sides of ∆ABC are proportional to the corresponding sides of ∆XYZ

AB/XY = AC/XZ = BC/YZ

3) Two sides in ∆ABC are proportional to two sides in ∆XYZ and the angles included between these sides in each triangle are equal.

AB/XY = AC/XZ and angle A = angle X.

Q: Determining whether two triangles are similar?

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Two equilateral triangles are always similar!

They are said to be similar but not congruent triangles.

for two similar triangles , their corresponding angles are equal.

Nope. You must know what it means to be similar. It means that ALL three angles are the same between two triangles. That been said, you can take any two random triangles, it's very likely that they are NOT similar.

To verify that two triangles are similar, you can use several similarity postulates and theorems. The most common ones include: **AA Similarity Postulate (Angle-Angle Similarity Postulate):** If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar. This postulate relies on the similarity of corresponding angles. **SAS Similarity Theorem (Side-Angle-Side Similarity Theorem):** If two pairs of corresponding sides of two triangles are in proportion, and their included angles are congruent, then the two triangles are similar. This theorem involves both sides and angles. **SSS Similarity Theorem (Side-Side-Side Similarity Theorem):** If the corresponding sides of two triangles are in proportion, then the two triangles are similar. This theorem only considers the proportions of the sides. These postulates and theorems are fundamental principles of triangle similarity and are used to establish whether two triangles are indeed similar. Remember that similarity means that the corresponding angles are equal, and the corresponding sides are in proportion.

Related questions

Two equilateral triangles are always similar!

They are said to be similar but not congruent triangles.

Not always, sometimes two obtuse triangles are similar and sometimes they are not similar.

Yes. You can even have two triangles with two pairs of sides that are the SAME measure without the triangles being similar.

If the angles of two triangles are equal the triangles are similar. AAA If you have three angles on both triangles these must be equal for the triangles to be similar. SAS If you have an angle between two sides and the length of the sides and the angle are the same on both triangles, then the triangles are similar. And SSS If you know the three sides

for two similar triangles , their corresponding angles are equal.

The triangles are similar, but not necessarily congruent.

DNA sequence similarity is the most useful factor in determining whether two organisms are related. The more similar the DNA sequences of two organisms are, the more closely related they are likely to be evolutionarily.

The term for two triangles that are congruent after a dilation is similar.

Nope. You must know what it means to be similar. It means that ALL three angles are the same between two triangles. That been said, you can take any two random triangles, it's very likely that they are NOT similar.

They're similar triangles.

It is given that two triangles are similar. So that the ratio of their corresponding sides are equal. If you draw altitudes from the same vertex to both triangles, then they would divide the original triangles into two triangles which are similar to the originals and to each other. So the altitudes, as sides of the similar triangles, will have the same ratio as any pair of corresponding sides of the original triangles.