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3 years ago

(GEOMETRY 100 POINTS)

Mathematics

2 answers:

Karo-lina-s [1.5K]3 years ago

5 0

Answer:

1) They are similar

2) 45 ft

Step-by-step explanation:

1) similar because both triangles have congruent interior angles

2) 75/35 = AB/21

AB = 45 ft

MariettaO [177]3 years ago

3 0

Answer:

Part A) Yes, Kayla can conclude that the triangles ABC and EDC are similar (see the explanation)

Part B) The width of the river is 45 feet

Step-by-step explanation:

The correct question is

(A) Can Kayla conclude that ΔABC and ΔEDC are similar? Why or why not?

(B) Suppose DE = 21 ft. What can Kayla conclude about the width of the river?

The picture in the attached figure

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

Part A) we know that

The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar

In this problem

$m\angle DCE=m\angle ACB$ -----> by vertical angles

$m\angle EDC=m\angle ABC$ -----> is a right angle

therefore

Triangles ABC and EDC are similar by AA Similarity Theorem

Part B) we know that

The triangles ABC and EDC are similar -------> see Part A

$\frac{BC}{DC}=\frac{AB}{ED}$

substitute the given values and solve for AB

$\frac{75}{35}=\frac{AB}{21}$

$AB=\frac{75}{35}(21)$

$AB=45\ ft$

therefore

The width of the river is 45 feet

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$\begin{array}{l}{\text { As } 1 \text { foot }=0.3048 \mathrm{m}} \\\\ {\Rightarrow 1 \text { foot } \times 1 \text { foot }=0.3048 \mathrm{m} \times 0.3048 \mathrm{m}} \\\\ {\Rightarrow 1 \text { foot } \times 1 \text { foot } \times 1 \text { foot }=0.3048 \mathrm{m} \times 0.3048 \mathrm{m} \times 0.3048 \mathrm{m}} \\\\ {=1 \mathrm{foot}^{3}=0.0283 \mathrm{m}^{3}} \\\\ {\Rightarrow 1 \text { cubic feet }=0.0283 \mathrm{m}^{3}}\end{array}$