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Delvig [45]
2 years ago
9

What criterion can be used to prove the triangles congruent with the given information?

Mathematics
1 answer:
djverab [1.8K]2 years ago
8 0

Answer:

D. none of these

Step-by-step explanation:

The image only shows two congruent angles/sides. In order for one of the given postulates to work, 3 congruent parts of the triangles must be applicable.

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Quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR
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Answer:

392

Step-by-step explanation:

Triangles XQP and YRS are right triangles because triples 6, 8, 10 are Pythagorean triples.

Extend lines XQ, YR, YS and XP and mark their intersection as A and B.

Quadrilateral XAYB is a square because all right triangles PXQ, QAR, RYS and SBP are congruent (by ASA postulate) and therefore

  • all angles of the quadrilateral XAYB are right angles
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Segment XY is the diagonal of the square XAYB, by Pythagorean theorem,

XY^2=XA^2+AY^2\\ \\XY^2=14^2+14^2\\ \\XY^2=196+196\\ \\XY^2=392  

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