Question

Problem 3-66

Examine each diagram below. Which diagrams are possible? Which are impossible? Justify each conclusion
Hint:

Answer 1

All of them is impossible in mathematics

Explanation:

In the first diagram we see a right triangle, which we can use pythagorean theorem to verify , but 20^2-14^2 does not equal to 5^2

IN the second diagram, According to the corresponding angles theorem, the statement “If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent” is true either way. But in the diagram we see 50 isn't equal to 48, hence it's a false statement too.

In the third diagram, we see we can verify it using the summation of triangle a+b+c=180, we clearly see 63+59+57 isn't equal to 180

So, indeed, all of the three diagram is impossible to exist in mathematics