Quickname: 3140

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

Junior High School, Middle School, High School.

Correct statements on the intercept theorems must be identified and marked.

A labeled drawing to illustrate the intercept theorems is shown. For this purpose a number of statements are presented with respect to the ratios of side lengths to each other, which represent applications of the intercept theorems.

Examples:

| ZA | / | ZA' | = | ZB | / | ZB' |

| BB' | / | ZA | = | AB'| / | AA' |

Some of the statements are correct and therefore statements of the intercept theorems, other statements are wrong. The correct statements have to be marked accordingly. Wrong statements are not only not of the queried type of theorem but are generally wrong. The number of presented statements is adjustable. If desired, an indication of the number of correct statements can be given.

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

Type of question

Open question, Multiple true statements, One true statement

Number of answers

2, 3, 4

Remark

Description

Name and direct link

Completion of a ratio equation, i.e. a rule of the intercept theorem.

In a statement of the intercept theorems the missing line segment name has to be inserted.

Application of the intercept theorems

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

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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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