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

4should be the last one n=4

Answer from: Quest

Here for a good time of free question

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