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EXTENDED RESPONSE Triangle A B C has vertices A(-3,-5), B(-1,-1) , and C(-1,-5) ,
Triangle X Y Z has vertices X(5,-5), Y(3,-1) , and Z(3,-5) ,
c. Write a logical argument using coordinate geometry to support your conjecture.

Respuesta :

The corresponding sides have the same measure and are congruent. So,  ΔABC ≅ ΔXYZ by SSS.

What in mathematics is the Pythagoras Theorem?

  • According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides.
  • The formula for this theorem is c2 = a2 + b2, where c is the hypotenuse and a and b are the triangle's two legs.

Observe the graph, the triangles are right triangles. In triangle ABC, AC = 2 and BC = 4. Use the Pythagorean

Theorem to find AB.

AB² = AC² + BC²

AB = √ AC² + BC²

AB = √ 2² + 4²

AB = √4 + 16

AB = √20

Similarly In triangle XYZ, ZX = 2 and ZY = 4. Use the Pythagorean Theorem to find XY

XY² = XZ² +  ZY²

XY = √ XZ² + ZY²

XY = √ 2² + 4²

XY = √4 + 16

XY =  √20

The corresponding sides have the same measure and are congruent. So,  ΔABC ≅ ΔXYZ by SSS.

Learn more about  Pythagoras theorem

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