Details for problem "Intercept theorem statements right or wrong"
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.
| 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.
Topics: Geometry Puzzles
Tags: Angle Division Rules
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Customization options for this problem
Number of problems
1, 2, 3, 4
Size of drawing
small, medium, large
Z,A,A',B,B', Pairs with ', All different
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
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.
Deutsche Version dieser Aufgabe