Question

Hello help me with this question thanks in advance​

Answer 1

`\bold{\huge{\underline{ Solution \: 1 }}}`

Basic theorems on similarity of triangles

Theorem 1 :- SSS Similarity

• When all the three sides of one triangle are in proportion to the other three sides of the another triangle then those 2 triangles are similar by SSS similarity .

Theorem 2 :- AA similarity

• When the two corresponding angles of one triangle are congruent to other two corresponding angles of another triangle then both the triangles are similar by AA Similarity .

Theorem 3 :- SAS similarity

• When the two sides of one triangle are in proportion to the other two sides of another triangle and the one of the angles of both the triangles that lie between two corresponding sides are equal then both the triangles are similar by SAS similarity.

Theorem 4 :- AAA similarity

• When all the three angles of one triangle are equal to other three angles of another triangle then both the triangles are similar by AAA similarity.

Let's Begin :-

Here, We have given statement that

• " If an angle of one triangle is congruent to an angle of another triangle and the corresponding sides including those angles are in proportion, then the two triangles are similar . "

From above theorem, we can conclude that

• Both the triangles are similar by SAS similarity

Hence, Option C is correct

`\bold{\huge{\underline{ Solution \: 2 }}}`

The given statement is proved by using Pythagorean theorem.

• Pythagorean theorem states that the square of hypotenuse that is longest side is equal to the sum of the squares of base and perpendicular height that is the smallest sides of the given triangle.

That is,

`\sf{\red{ (Hypotenuse)^(2) = ( Perpendicular)^(2) + ( Base) ^(2)}}`

Hence, Option D is correct that is Pythagorean theorem.