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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.
b. If A C=1300 meters, D C=550 meters, and D E=851.5 meters, what is AB? Explain your reasoning.

Respuesta :

The value of line AB is 550 meters.

What do we presume by the congruency of a triangle?

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

So,

First, we'll prove that △BEA ≅ △DEC.

  • ∠A = ∠C = (BA and CD is ⊥ AC)
  • AE = CE = (E is the midpoint of AC)
  • ∠AEB = ∠DEC = (Inversely opposite angles)

So, △BEA ≅ △DEC is under ASA condition.

  • Then, DC is identical to AB.

Therefore, the value of AB is 550 meters.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

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