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 $a^2+b^2=c\cdot c=c^2$ .

7 0

3 years ago

Read 2 more answers

Beverley has quarters and dimes in her pocket. She has 21 coins with a total value of $3.00. How many of each type of coin does

forsale [732]

Answer:

6 quarters and 15 dimes

Step-by-step explanation:

6 quarters = $1.50

15 dimes = $1.50

6 quarters + 15 dimes = $3.00

8 0

3 years ago

Please help!!

Inessa05 [86]

Let the width = w.
The length is 6 times the width, so the length is 6w.
The perimeter is 70.
P = 2L + 2W

70 = 2(6w) + 2(w)

70 = 12w + 4w

70 = 14w

5 = w

The width is 5.
The length is 6 times the width, so the length is 6 * 5 = 30

Area of rectangle = LW

A = 5 * 30 = 150

8 0

3 years ago