Mathematics, 15.07.2019 17:30 Fatimaneedhelp

Rex, paulo, and ben are standing on shore watching for dolphins. paulo sees one surface directly in front of him about a hundred feet away. use the spaces provided below to prove that the square of the distance between rex and ben and the dolphin, and ben and the dolphin. urgent i need to pass this to graduate

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1. $m\angle BAC=m\angle CAD,\ m\angle ACB=m\angle ADC=90^{\circ}$ , then $m\angle ABC=m\angle ACD$ and triangles ADC and ACB are similar by AAA theorem.

2. The ratio of the corresponding sides of similar triangles is constant, so

$\dfrac{AC}{AB}= \dfrac{AD}{AC}$ .

3. Knowing lengths you could state that $\dfrac{b}{c}= \dfrac{e}{b}$ .

4. This ratio is equivalent to b^2=ce .

5. $m\angle ABC=m\angle CBD,\ m\angle ACB=m\angle CDB=90^{\circ}$ , then $m\angle BAC=m\angle BCD$ and triangles BDC and BCA are similar by AAA theorem.

6. The ratio of the corresponding sides of similar triangles is constant, so

$\dfrac{BC}{BD}= \dfrac{AB}{BC}$ .

7. Knowing lengths you could state that $\dfrac{a}{d}= \dfrac{c}{a}$ .

8. This ratio is equivalent to a^2=cd .

9. Now add results of parts 4 and 8:

b^2+a^2=ce+cd .

10. c is common factor, then:

b^2+a^2=c(e+d) .

11. Since e+d=c you have $a^2+b^2=c\cdot c=c^2$ .

Answer from: lcyaire

Given information: $\triangle ADC\sim \triangle ACB$ and $\triangle BDC\sim \triangle BCA$ .

To Prove : a^2+b^2=c^2

Proof:

Statement Proof

1. $\triangle ADC\sim \triangle ACB$ 1. Given

2. $\dfrac{AC}{AB}=\dfrac{AD}{AC}$ 2. The ratio of corresponding parts of similar triangles is a constant

3. $\dfrac{b}{c}=\dfrac{e}{b}$ 3. Rewrite statement 2 using given side labels.

4. b^2=ce 4. Cross multiply statement 4

5. $\triangle BDC\sim \triangle BCA$ 5. Given

6. $\dfrac{BC}{BA}=\dfrac{BD}{BC}$ 6. The ratio of corresponding parts of similar triangles is a constant

7. $\dfrac{a}{c}=\dfrac{d}{a}$ 7. Rewrite statement 5 using given side labels.

8. a^2=cd 8. Cross multiply statement 7

9. a^2+b^2=cd+ce 9. Add statement 4 and 8

10. a^2+b^2=c(d+e) 10. c is common factor

11. a^2+b^2=c^2 11. Segment addition property.

Hence proved.

Answer from: Quest

so the perpendicular line goes through the given pointyou would get a perpendicular line at some random location

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.

Answer from: Quest

i need points

step-by-step explanation:

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