Marking ! plus 30pts asapp

1. write an inequality for the range of the third side of a triangle if two sides measure 4 and 13.

2. if lm = 12 and nl = 7 of ∆lmn, write an inequalty to describe the lenght of mn.

3. use the hinge theorem to compare the measures of ad and bd.

  1.  9 < s < 17

  2.  5 < MN < 19

  3.  AD > BD

Step-by-step explanation:

1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:

Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...

  9 < s < 17

(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)

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2. Same as (1) using different numbers.

  12 -7 < MN < 12 +7

  5 < MN < 19

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3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:

  AD > BD

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step-by-step explanation:

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