Question

Following the route​ shown, what is the total distance traveled by the architectural tour if it ends where it​ started? What properties and theorems did you use to find the​ distance?
Using, -------------------- it can be shown that the two triangles formed are congruent. Then using ,---------------------------- the length of the road from the intersection to the first turn can be found to be ---------------------- feet. Thus, the total length of the tour is --------------- feet.
Answer's first blank:
Side-Angle Side
CPCTC
Side- Side - Side
Answer's second blank:
Side- Side - Side
CPCTC
Side-Angle Side

Answer 1

Using, SAS it can be shown that the two triangles formed are congruent. Then using ,-CPCTC the length of the road from the intersection to the first turn can be found to be 200 feet. Thus, the total length of the tour is 1,700 feet.

What is SAS?

The SAS Triangle Theorem indicates that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.

By the use of the corresponding parts of congruent triangles are congruent (CPCTC) rule, we can state that the missing side is 200 feet. If that is the case, then the total distance traveled can be obtained by adding all the lengths of triangles:

=200 + 200 + 300 + 350 + 350 + 300

= 1,700 feet.

Hence, te total length of the tour is 1,700 feet.

Learn more about CPCTC:
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Answer 2

The theorems used are:

First blank: side-angle-side theorem

Second blank: CPCTC

Third blank: 200 feet

Fourth blank: 1,700 feet.

What is the Side-angle-side Congruence Theorem (SAS):

Wen two triangles have a pair of included congruent angles and two pairs of corresponding congruent sides, then both triangles are congruent to each other by the side-angle-side theorem.

Furthermore, if two triangles are known to be congruent to each other, the CPCTC states that "corresponding parts of corresponding triangles are congruent". This means all angles and all sides that corresponds to each other are congruent.

Therefore:

Using the side-angle-side theorem it can be shown that the two triangles are congruent to each other.

Then using CPCTC , the length of the road from the intersection to the first turn would be 200 feet.

The total length of the tour would be = 2(200 + 300 + 350)

= 1,700 feet.

Learn more about the side-angle-side theorem on:

brainly.com/question/10617589

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