2. the coordinates of the vertices of abc are a (5, 2), b (2, 4), and c (7, 5). determine whether abc is a right triangle.

3. the coordinates of the vertices of quadrilateral qrst are q (5, 1), r (8, 7), s (14, 10) and t (10, 2). iron man states that quadrilateral qrst is a parallelogram. prove or disprove iron man’s statement. explain your method (fill out the brainstorming area) and show your work.

Part 2) Triangle ABC is a right triangle (see the explanation)

Part 3) Quadrilateral QRST is not a parallelogram (see the explanation)

Step-by-step explanation:

Part 2) we have

A (5, 2), B (2, 4), and C (7, 5)

Plot the figure to better understand the problem

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

step 1

Find the length side AB

A (5, 2), B (2, 4)

substitute the values in the formula

step 2

Find the length side BC

B (2, 4), C (7, 5)

substitute the values in the formula

step 3

Find the length side AC

A (5, 2), C (7, 5)

substitute the values in the formula

step 4

Verify if the triangle ABC is a right triangle

we know that a right triangle must satisfy the Pythagorean Theorem

so

Remember that the hypotenuse is the greater side

substitute the values

----> is true

therefore

Triangle ABC is a right triangle

Part 3) we have

Q (5, 1), R (8, 7), S (14, 10) and T (10, 2)

we know that

The opposite sides of a parallelogram are parallel and congruent

the formula to calculate the distance between two points is equal to

Step 1

Find the length side QR

Q (5, 1), R (8, 7)

substitute in the formula

Step 2

Find the length side RS

R (8, 7), S (14, 10)

substitute in the formula

Step 3

Find the length side ST

S (14, 10), T (10, 2)

substitute in the formula

Step 4

Find the length side QT

Q (5, 1), T (10, 2)

substitute in the formula

Step 5

Compare the length of the opposite sides

QR and ST

RS and QT

Opposite sides are not congruent

therefore

Quadrilateral QRST is not a parallelogram

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: