We know that The triangle inequality states that for any triangle, the sum of the lengths of any two sides of a triangle<span> is greater than the length of the third side </span> Part 1) <span>Which of the following sets of possible side lengths forms a triangle? case A) </span><span>6, 9, and 15 6+9 is not > 15
case B) </span><span>4, 10, and 15 4+10 is not > 15
case C) </span><span>10, 15, and 25 10+15 is not > 25
case D) </span><span>12, 12, and 23 12+12 is > 23-----> ok 12+23 is > 12----> ok
the answer part 1) is </span>12, 12, and 23 <span> Part 2) </span><span>Which of the following sets of possible side lengths forms a right triangle? </span><span> case A) </span><span>12, 35, and 38 </span>if the side lengths forms a right triangle then 12²+35²=38² 12²+35²------> 1369 38²------> 1444
1369 is not equal to 1444
case B) 11,<span>60, and 61 </span>if the side lengths forms a right triangle then 11²+60²=61² 11²+60²-------> 3721 61²------> 3721 3721 is equal to 3721------> the sides forms a right triangle
case C) 9,40<span> and 45 </span>if the side lengths forms a right triangle then 9²+40²=45² 9²+40²------> 1681 45²------> 2025 1681 is not 2025
case D) <span>6, 12, and 13 </span>if the side lengths forms a right triangle then 6²+12²=13² 6²+12²------> 180 13²--------> 169 180 is not 169
the answer part 2) is case B) 11,60, and 61 forms a right triangle
Part 3) <span>Which of the following sets of sides does not form a right triangle?
case A) </span><span>6, 8, 10 </span>if the side lengths forms a right triangle then 6²+8²=10² 6²+8²------> 100 10²-------> 100 100 is equal to 100 ------> the side lengths forms a right triangle
case B) 8,15,17 if the side lengths forms a right triangle then 8²+15²=17² 8²+15²------> 289 17²-------> 289 289 is equal to 289-----> the side lengths forms a right triangle
case C) 7,24,26 if the side lengths forms a right triangle then 7²+24²=26² 7²+24²------> 1176 26²--------> 676 1176 is not 676-----> the sides lengths does not form a right triangle
case D) 5,12,13 if the side lengths forms a right triangle then 5²+12²=13² 5²+12²-------> 169 13²-------> 169 169 is equal to 169------> the side lengths forms a right triangle
the answer Part 3) is the option 7,24,26 does not form a right triangle
Polygons (shapes made of straight lines) where no angle is greater than 180 degrees. If even one angle is greater than 180 then it is a concave polygon.
