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

Answers: 1

Show answers

Answers

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

step-by-step explanation:

Answer from: Quest

17 x 256=4352

sorry if this is wrong, i'm new.

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 17:30, alexandroperez13

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. find the probability that a randomly selected bill will have an amount greater than $155, which the city believes might indicate that someone is wasting water. would a bill that size be considered unusual?

Answers: 2

continue

Mathematics, 21.06.2019 19:00, jdkrisdaimcc11

Atheater wants to build movable steps that they can use to go on and off the stage. they want the steps to have enough space inside so they can also be used to store props. how much space is inside the steps?

Answers: 1

continue

Mathematics, 21.06.2019 20:00, soniah

Pepe and leo deposits money into their savings account at the end of the month the table shows the account balances. if there pattern of savings continue and neither earns interest nor withdraw any of the money , how will the balance compare after a very long time ?

Answers: 1

continue

Mathematics, 22.06.2019 01:50, talia43

What will be the end result for the taxpayer who filed his federal income tax return using the 1040ez form shown belowa he'll owe $173b he'll receive a refund of $173c he'll owe $3921d he'll receive a refund of $3921

Answers: 2

continue

You know the right answer?

Rex, paulo, and ben are standing on shore watching for dolphins. paulo sees one surface directly in...