Geometry: Collinearity, Betweenness, and Assumptions (Level 3 of 4)

The video tutorial covers three examples illustrating the concepts of colinearity and triangle inequality. The first example involves finding the length of a segment using given ratios and algebraic expressions. The second example focuses on solving for a variable in a collinear point scenario. The final example uses triangle inequality to determine possible lengths of a triangle's side. Each example is explained step-by-step, emphasizing the application of geometric and algebraic principles.

What is the length of segment WX if the length of segment WY is 25 and the ratio of WX to XY is 3:2?

• 25

• 20

• 15

• 10

If the ratio of WX to XY is 3:2, and WX is expressed as 3X, what is XY expressed as?

• 4X

• 3X

• 2X

• X

If the length of segment GE is 3Y and the length of segment GH is 7Y - 4, what is the value of Y if EH is 24?

• 6

• 8

• 5

• 7

In a triangle, if the length of segment AB is 6 and BC is 9, what is the maximum possible length of segment AC?

• 18

• 10

• 12

• 15

What is the minimum possible length of segment AC in a triangle where AB is 6 and BC is 9?

• 3

• 5

• 2

• 4

Which of the following is NOT a valid inequality for the sides of a triangle?

• BC + AC > AB

• AC + AB > BC

• AB + AC < BC

• AB + BC > AC

In the context of triangle inequalities, which statement is true?

• The sum of any two sides must be less than the third side.

• The sum of any two sides must be greater than the third side.

• The sum of any two sides must be equal to the third side.

• The sum of any two sides must be twice the third side.