Question

Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13

Answer 1

Please see attached file for the triangle’s figure:

 

Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).

Therefore, the inequality that she will use to contradict the assumption is 4:9 ≠ 6:13.

To add, a relation that holds between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.

Inequalities are governed by the following properties:

Transitivity
 Converse
 Addition and subtraction
 Multiplication and division
 Additive inverse
 Multiplicative inverse
Applying a function to both sides

Answer 2

Answer:

4:9 ≠ 6:13.

Step-by-step explanation: