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A surveyor needs to find the distance from point A to point B across a canyon. She places a stake at A, and a coworker places a stake at B on the other side of the canyon. The surveyor then locates C on the same side of the canyon as A such that CA ⊥ AB. A fourth stake is placed at E, the midpoint of CA. Finally, a stake is placed at D such that CD ⊥ CA and D,E, and B are sited as lying along the same line.
a. Explain how the surveyor can use the triangles formed to find AB.

Respuesta :

The surveyor can find AB if he finds CD as CD = AB.

What actually means by a triangle's congruency?

  • Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.
  • These triangles can be moved, rotated, flipped, and turned to appear identical.
  • If they are readjusted, they will coincide.
  • Two triangles are congruent if they satisfy all five congruence conditions.
  • They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).

So,

First, connect B and D and make a square ACDB with BC as a diagonal.

  • In triangle ACB and DCB:
    CB = CB = (Common)
  • AB = CD = (Parallel)
  • So, angle ABD = angle BCD (Alternate exterior angles)

So,  ACB ≅ DCB under SAS condition.

Therefore, the surveyor can find AB if he finds CD as CD = AB.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

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