The definition of similar triangles says that 2 triangles are similar if they have the same shape but different size. There are two criteria to check for this:
1) If all angles in one triangle are equal to the angles in another one, then the 2 are equal.
2) If the sides have the same proportions, then the 2 triangles are similar.
1) We have that all the angles of the 2 triangles have an equal angle in the other triangle. In specific, Q is matched to B, P to A and R to C. Hence, since corresponding angles are congruent, the two triangles are similar.
2) Here we are given information about the sides of the triangles, so we will check the second criterion. We form the ratio of the largest sides of each trangle and the shortest sides. 30/5=6. For the shortest sides, 18/3=6. Finally for the middle sides, 24/4=6. Hence, we have that the triangles are similar since the ratios are equal. (it doesn't matter whether we take the bigger or the smaller side as a numerator, as long as we are consistent).
The distance between those to points is d=6.708204 or d=6
Answer:
The answer to this problem is 4
Step-by-step explanation:
Because he has 4 pounds of apples left, you are to subtract that from the total pounds picked, which was a total of 55 pounds. So 55 with 4 taken away, or 55 - 4, equals 51. Since he had equally put 51 pounds into six bags, you are to then divide . 51 / 6 = 8.5. He had put 8.5 pounds worth of apples into each bag.
Answer:
Step-by-step explanation:
Given: Trey's test score average decreased by 14 points this semester.
To find: a signed number to represent this change in average.
Solution:
The decrease can be denoted by minus 
sign and increase can be denoted by plus 
sign.
So, a signed number to represent the change in test score average is
