Question

Consider the following two statements:

1. The median to the hypotenuse of any right triangle is half as long as the hypotenuse.
2. If three or more parallel lines intercept congruent segments on one transversal, they intercept congruent segments on any transversal.
Which of the following is true?
A) Statement 1 is true.
B) Statement 2 is true.
C) Both statements 1 and 2 are true.
D) Neither statement 1 nor 2 is true.

Answer 1

Statement 1 is true and statement 2 is true.

Step-by-step explanation:

In statement 1, the median to the hypotenuse of any right triangle is indeed half as long as the hypotenuse. This is because the median to the hypotenuse is equal to half of the hypotenuse. This can be proven using the Pythagorean theorem.

In statement 2, if three or more parallel lines intercept congruent segments on one transversal, they will also intercept congruent segments on any other transversal. This is a property of parallel lines called the Transversal Postulate.

Therefore, the correct answer is C) Both statements 1 and 2 are true.