Question

Geometry: CC 2015 > Chapter 2: Chapter 2 Test >

Answer 1

Answer:

The area of ABCF is 2 and 2 × AB = 4

The statement proves that the conjecture is false

Step-by-step explanation:

A conjecture is a proposition or conclusion that is presumed to be true or correct but which is based on incomplete details or information

Given the length of the sides of rectangle ABDE, we have;

Length AB = 2 units

Length DE = 2 units

The area of ABDE = 2 × 2 = 4 unit²

Therefore, the area of the rectangle ABDE is equal to 2 × the length of either AB or DE

However, the are of rectangle ABCF = 2 × 1 = 2 unit²

While the area of rectangle 2 × the length of side AB = 2 × 2 = 4 unit², which is not equal to the number of square units in the area of the rectangle.

Therefore;

The area of ABCF is 2 and 2 × AB = 4

The statement (above) proves that the conjecture is false.