Question

write tests of similarity of triangles AAA test, SAS test, AA test ,SSS test​

Answer 1

Answer:

AA (or AAA) or Angle-Angle Similarity

If in two Triangles corresponding angles are equal then their corresponding sides are in the same ratio (or proportional ) and hence the two Triangles are similar

SAS or Side-Angle-Side Similarity

If one angle of a Triangle is equal to one angle of the other triangle and the sides including these angles are proportional then the two Triangles are similar

SSS or Side-Side-Side Similarity

If in two Triangles sides of One triangle are proportional to (ie, in the same ratio of) the site of the Other triangle then their corresponding angles are equal and hence the two Triangles are similar

Step-by-step explanation:

AA (or AAA) or Angle-Angle Similarity

If in two Triangles corresponding angles are equal then their corresponding sides are in the same ratio (or proportional ) and hence the two Triangles are similar

From the figure given above, if ∠ A = ∠X and ∠C = ∠Z then ΔABC ~ΔXYZ.

From the result obtained, we can easily say that,

AB/XY = BC/YZ = AC/XZ

and ∠B = ∠Y

SAS or Side-Angle-Side Similarity

If one angle of a Triangle is equal to one angle of the other triangle and the sides including these angles are proportional then the two Triangles are similar

Thus, if ∠A = ∠X and AB/XY = AC/XZ then ΔABC ~ΔXYZ.

From the congruency,

AB/XY = BC/YZ = AC/XZ

and ∠B = ∠Y and ∠C = ∠Z

SSS or Side-Side-Side Similarity

If in two Triangles sides of One triangle are proportional to (ie, in the same ratio of) the site of the Other triangle then their corresponding angles are equal and hence the two Triangles are similar

Thus, if AB/XY = BC/YZ = AC/XZ then ΔABC ~ΔXYZ.

From this result, we can infer that-

∠A = ∠X, ∠B = ∠Y and ∠C = ∠Z

Answer 2

The AAA, SAS, AAS, and SSS test of similarity of triangles are given below:

• Two triangles are said to be congruent if all of their corresponding sides and angles are equal. These triangles would fit perfectly one above one another. The congruency of two triangles can be proved using the following tests:
• AAA (angle-angle-angle) test: Two triangles are said to be congruent by the angle-angle-angle (AAA) test if every angle in one triangle is equal to the corresponding angles in the other triangle.
• SAS (side-angle-side) test:  If two corresponding sides of the two triangles are equal and the angle between the two sides of one triangle is equal to that in the other triangle, we that the triangles are congruent using the side-angle-side (SAS) test.
• AAS (angle-angle-side) test: If two corresponding angles of a triangle are equal and the side not included between these angles is equal to the corresponding side of the other triangle, then the triangles are to be congruent using the  AAS (angle-angle-side) test.
• SSS (side-side-side) test: If each side of a triangle is equal to the corresponding sides of the other triangle, the triangles are said to congruent using SSS (side-side-side) test.

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