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.

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

- Set up the equation of proportion according to the radiation theorems.
- Solve the equation for x
- 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.

Examples:

| 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

- fixed to Z for the intersection of the lines, A and A' for the points on one line and B and B' for the points on the other line.
- random for the intersection, and random pairs of X and X' for both lines.
- completely random, each point is labeled individually.

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

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Parameter

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

Remark

Description

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.

You may pass on the worksheets offered for download on this page to others, but not modify or sell them.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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