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question:
1. Use the Pythagorean theorem to find AD.
2. Find AC. Show your work.
3. Is ΔABC a right triangle? Explain.
SHOW YOUR WORK

Problem 1

Answer: AD = 9

-------------------------------------------------

Work Shown:

Focus on triangle ADB, which is the smaller triangle on the left.

We have these side lengths

AD = unknown leg

BD = 12 = known leg

AB = 15 = known hypotenuse

Let's apply the Pythagorean Theorem to find the unknown leg

a^2 + b^2 = c^2

(AD)^2 + (BD)^2 = (AB)^2

(AD)^2 + (12)^2 = (15)^2

(AD)^2 + 144 = 225

(AD)^2 = 225-144

(AD)^2 = 81

AD = sqrt(81)

AD = 9

Side AD is 9 units long.

========================================================

Problem 2

Answer: AC = 25

-------------------------------------------------

Work Shown:

AC = AD + DC .... segment addition postulate

AC = 9 + 16 ..... substitution; refer to problem 1

AC = 25

========================================================

Problem 3

Answer: Triangle ABC is a right triangle.

-------------------------------------------------

Work Shown:

The Pythagorean Theorem Converse says "if a^2+b^2 = c^2 is a true equation, then the triangle with sides a,b,c is a right triangle". Keep in mind that c is always the longest side (hypotenuse). The order of 'a' and b doesn't matter. Convention has us usually do [tex]a \le b[/tex] but again the order isn't important.

We have these three sides

Plug those values into the equation below. Simplify each side.

a^2+b^2 = c^2

15^2 + 20^2 = 25^2

225 + 400 = 625

625 = 625

We get a true equation. Therefore, triangle ABC is a right triangle.

Answer:

Step-by-step explanation:

Pythagorean = c^2 =a^2 + b^2

we are given c and a   so solve for b

c^-a^2 = b^2

15^2- 12^ = b^2

81= b^2

[tex]\sqrt{81}[/tex]=b

9=b

AD=b

AC = AD + 16

AC =9 + 16 =25

if it's a right triangle then Pythagorean will work with the sides to make 25

AC^2 = 15^2+20^2

AC = [tex]\sqrt{625}[/tex]

AC = 25

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