Two figures are said to be similar if they have the same shape and necessarily not the same size. For example, we can say all circles are similar. All squares are similar and equilateral triangles are similar. All congruent figures are similar but similar figures need not be congruent. In this article, we will learn the properties of similar triangles.
What are the Properties of Similar Triangles
Property 1:
Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.
Consider two triangles DEF and RST.
ΔDEF ~ ΔRST
∠D = ∠R, ∠E = ∠S and ∠F = ∠T
DE/RS = EF/ST = DF/RT.
*The ratio is called the scale factor. The symbol ~ is used to denote similarity.
Property 2:
If the corresponding angles of two triangles are equal, then the triangles are similar. They are called equiangular triangles. A famous Greek mathematician Thales gave an important result relating to two equiangular triangles. He used a result called the Basic Proportionality Theorem, which is known as the Thales Theorem.
Example
Given ΔABC ~ ΔXYZ. If AB = 4 cm, BC = 5 cm, AC = 6 cm and XY = 8 cm find YZ and XZ.
Solution:
ΔABC ~ ΔXYZ
So AB/XY = BC/YZ = AC/XZ
4/8 = 5/YZ
YZ = 8×5/4 = 10 cm
4/8 = 6/XZ
XZ = 8×6/4 = 12 cm
To Know how to Find the Area Of Similar Triangles, Watch The Below Video:
Frequently Asked Questions
What do you mean by Similar triangles?
If the corresponding angles of two triangles are equal and corresponding sides are in the same ratio or proportion, then those triangles are similar.
What are the 3 Similar Triangle theorems?
SAS or Side-Angle-Side Similarity theorem, SSS or Side-Side-Side Similarity theorem, and AA or AAA or Angle-Angle Similarity theorem are the three Similar Triangle theorems.
State the SAS Similarity theorem.
SAS Similarity theorem states that if the two sides of a triangle are in the same proportion to the two sides of another triangle, and the angle included by the two sides in both the triangles are same, then two triangles are similar.
State the SSS Similarity theorem.
SSS Similarity theorem states that if all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.
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