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Details for problem "Determine line segment length with intercept theorem"

Quickname: 8979

Suitable for K-12 grades: Grade 7 Grade 8 Grade 9

Junior High School, Middle School, High School.


In application of the intercept theorem the fourth line segment length is to be calculated from three given lengths.


In application of the intercept theorem the fourth line segment length is to be calculated from three given lengths. (Example for this math problem) In application of the intercept theorem the fourth line segment length is to be calculated from three given lengths. (Example for this math problem)


A labeled drawing to illustrate the intercept theorems is shown. On the figure three lines are labeled with their length. The inscription does not correspond to the actual length. Therefore no lengths are to be determined by measurement. However, the relations of the line segments to each other are correct.

The task is to calculate the length of the fourth line segment, which is labeled with the letter "x".

One of the intercept theorems is to be used for this. If desired, a reference to the intercept theorems can also be included in the problem definition.

To do so the following three steps are necessary

  1. Set up the equation of proportion according to the radiation theorems.
  2. Solve the equation for x
  3. Calculate the solution.

These steps are shown in the solution. The problem can be set so that these steps are also given in the assignment.


     | ZA | / | ZA' | = | ZB | / | ZB' |
        x / 5 = 7 / 14   
        x = 7 * 5 / 14

        x = 2.5

Which theorems are tested is configurable. The figure is presented according to the queried ray-set: For the first and second theorem the figure has two straight lines or rays, for the third theorem three. The figure can be drawn in V-shape, X-shape, or in a random selection of both variants.

The inscription of the points can be optionally

The size of the drawing can be selected in several steps. The number of problems can also be configured.

Topics: Geometry

Tags: Angle Division Rules

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Customization options for this problem

Possible values
Number of problems
1, 2, 3, 4
Size of drawing
small, medium, large
Point names
Z,A,A',B,B', Pairs with ', All different
Theorems covered
First, second, third, First, Second, Third, First & second, First & third, Second & third
Type of drawing
V or X, V, X
Mention intercept theorems
No reference, General reference, Show calculation steps

Similar problems

Name and direct link
Without actually calculating any lengths
In a statement of the intercept theorems the missing line segment name has to be inserted.
Knowledge of the rules, i.e. the equations of ratios
Correct statements on the intercept theorems must be identified and marked.

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Deutsche Version dieser Aufgabe
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