write difference between congruent and similar triangle write basic properties theorem and converse all basic theroem properties and prove also
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Answer:
Basic Properties of similar triangle
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.
There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.
SSS (side, side, side) SSS stands for "side, side, side" and means that we have two triangles with all three sides equal. ...
SAS (side, angle, side) ...
ASA (angle, side, angle) ...
AAS (angle, angle, side) ...
HL (hypotenuse, leg)
Different between similar and CONGRUENT triangle
Similar means that only the angles are the same, but the sides are not. Congruent means the angles and sides are the same.
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Basic proportionality theorem was proposed by a famous Greek mathematician, Thales, hence, it is also referred to as the Thales theorem. According to the famous mathematician, for any two equiangular triangles, the ratio of any two corresponding sides of the given triangles is always the same. Based on this concept, the basic proportionality theorem(BPT) was proposed. It gives the relationship between the sides of any two equiangular triangles.
The concept of Thales theorem has been introduced in similar triangles. If the given two triangles are similar to each other then,
Corresponding angles of both the triangles are equal
Corresponding sides of both the triangles are in proportion to each other
The theorem thus also helps us better understand the concept of similar triangles. Now let us try and understand the Basic Proportionality Theorem.