Question

"Penny wrote the following statements:

Statement 1: Perpendicular lines are two lines that intersect at 90° angles.
Statement 2: If two lines intersect, then they intersect at exactly one point.
Which geometry term does each statement represent?
Group of answer choices
a. Statement 1: postulate; Statement 2: theorem
b. Statement 1: theorem; Statement 2: postulate
c. Statement 1: definition; Statement 2: theorem
d. Statement 1: postulate; Statement 2: definition"

Answer 1

Statement 1 defines perpendicular lines as intersecting at 90-degree angles, which is a geometric definition. Statement 2 describes a basic postulate of Euclidean geometry, known as the intersection postulate, that two lines intersect at exactly one point.

Step-by-step explanation:

Penny wrote two statements aimed to represent geometric concepts:

1. Perpendicular lines are two lines that intersect at 90° angles.
2. If two lines intersect, then they intersect at exactly one point.

The first statement defines perpendicular lines, and this is a basic definition within geometry that specifies the nature of their intersection. The concept of lines intersecting at exactly one point is a fundamental postulate in Euclidean geometry, often referred to as the uniqueness of intersection or the intersection postulate.

Therefore, the correct answer to what each statement represents would be:

1. Statement 1: definition
2. Statement 2: postulate

Thus, the geometry term represented by each statement, in the options provided, is (c) Statement 1: definition; Statement 2: theorem, although the second statement would more accurately be described as a postulate.