Help me solve this problem its urgent. In the above given figure( attached photo) , M is the point on side QR. Fill in the blanks using symbol =, > or < to complete the statement.

1) PM _ PQ + QM
2) PM _ PR + MR
3) PM _ 1/2 (PQ+PR+QR)

1) PM < PQ + QM

2) PM < PR + MR

3) PM < 1/2 (PQ + PR + QR)

Step-by-step explanation:

This problem is based on the Pythagorean Theorum Equation

which states that a right triangle with sides a, b and hypotenuse can be written mathematically as hypotenuse =

We can rewrite each line segment of the diagram into variables to simplify this problem and use the Pythagorean equation:

Line PQ = Hypotenuse 1, Line PR = Hypotenuse 2, Line PM = Side B, Line QM = Side A, Line MR = Side C

With all the line segments simplified into variables you can separate the diagram into 2 seperate triangles. Triangle 1 has H1, A, B and Triangle 2 has H2, C, B

Using the Pythagorean equation for both triangles you get:

H1 =   and H2 =  

Now you can assign random values for each variable and compare the problem statements.

For Triangle 1 lets assign variables A = 1, B = 2, and H1 = = = 1.73  For Triangle 2 lets assign variables C = 3, B = 2 and H2 = = 3.6  

For the final step you can directly compare the statements and see which symbol is correct.

1) B ____ H1 + A is equivalent to  2  ____ (1.73 + 1),  which is turns out to be  2 < 2.73   The answer is  <

2) B ____ H2 + C is equivalent to 2 ____ (3.6 + 3), which turns out to be

2 < 6.6    The answer is < again

3) B ____ 1/2 (H1 + H2 + (A+C)  is equivalent to  2 _____ [1/2] (1.73 + 3.6 + 1 + 3), which turns out to be  2 < 4.67     The answer is <  again

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (