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Angle Angle Similarity

Introduction to angle angle similarity:

In this following article we are going to see about the Angle Angle symmetry postulate. By using this postulate we can check the congruency of the triangles. According to the postulate two triangles are congruentwhen two angles of both triangles are congruent. If two lines are cut by a transversal line then the corresponding angles are congruent and the lines are parallel.



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Angle Angle similarity:


Whentwo parallel lines are cut by a transversal, the pairs of their corresponding angles are congruent. When two lines are cut by a transversal line the corresponding angles will be congruent, and the lines are said to be parallel.

When any two angles of one triangleare congruent to the corresponding two angles of another triangle, the triangles are said to be similar. Also in a quadrilateral if both pairs of opposite angles are congruent, the quadrilateral is nothing but a parallelogram.

 

InGeneral, similar triangles are triangles that have the same shape. One triangle is up to scale of another. For any triangle, the shape is determined by its angles. For two triangles and to be similar if theysatisfy any of the following conditions:

1. Corresponding sides of the triangles will have lengths in the same ratio:

In other words this can be said that the one triangle is an enlargement of another.

2.Angle ABC is equal to the measure of Angle EDF , and Angle ABC is equal to measure of angle of DEF. This can also be applied to, angle of ACB is equal to angle of DFE.

Two congruent triangles ABC and DEF can also be written as

 `Delta` ABC`~~` `Delta` DEF

Insimilar triangles we know that two pair of angle are same. Then the third pair of angles must also be equal. When all the three angle pairs are equal, then the three pairs of sides of the two triangles must also be in proportion.


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Example Problems on angle angle similarity:


1. Given that the two angles in two triangles are 60, 50 and 50, 60. Are these triangles similar?

Answer: According to angle angle similarity postulate when two triangles are equal then two triangles are similar.

2. Given that the two angles in two triangles are 45, 65 and 45, 65. Are these triangles similar? Find third angle pair.

Answer: According to angle angle similarity postulate when two triangles are equal then two triangles are similar.

Total angle in triangle is 180.

45 + 65 + x = 180

x + 110 = 180

x = 180 - 110

x=70 degrees.