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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

AD = 9

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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.

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Problem 2

AC = 25

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Work Shown:

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

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

AC = 25

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Problem 3

Triangle ABC is a right triangle.

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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 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.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

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step-by-step explanation: