Q is between P and R . S is between Q and R, and R is...

$Q$ is between $P$ and $R . S$ is between $Q$ and $R,$ and $R$ is between $Q$ and $T . P T=34$ $Q R=8,$ and $P Q=S Q=S R .$ What is the length of $\overline{R T} ?$
$\begin{array}{lllllll}
\text { A } & 9 & \text { B } 10 & \text { C } & 18 & \text { D } & 22
\end{array}$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Collinearity and Linear Order of Points

This concept involves understanding that certain points lie on the same line and that the order of these points matters. In problems where points are stated to be 'between' two others, it is important to grasp how the relative positions of points determine which segment lengths add up to form the total distance between the endpoints.

Segment Addition Postulate

This principle states that if a point lies between two other points on a line, then the total distance between the endpoints is equal to the sum of the distances of the segments into which the point divides the line. It is used to set up equations that relate the whole segment to its parts.

Equality of Segments

In many geometry problems, certain segments are given as equal. Recognizing and using the property that equal segments have the same length allows one to assign the same variable to these segments, which simplifies the process of setting up and solving algebraic equations that represent distance relationships.

Algebraic Representation of Geometric Relationships

This concept involves translating geometric conditions, such as lengths of segments and their relationships, into algebraic equations. By assigning variables to unknown segment lengths and using known segment measures, one can solve for the unknowns using algebraic methods.

Transcript

Please give Ace some feedback