# Assumptions about Diagrams

Lesson Plans > Mathematics > Geometry > LogicPrint

## Assumptions about Diagrams

One thing that many geometry textbooks don't adequately address is the question of what kinds of assumptions we can make based on a diagram that is given to us in a problem. Most books will emphasize that diagrams are not drawn to scale, and students may be left thinking that you can't assume *anything* based on a diagram. However, this is not the case. So we spend some time early on discussing the do's and don'ts of diagram interpretation.

**Assumptions you can't make**

- If two segments look congruent, you may not assume that they are.
- If two segments don't look congruent, you may not assume that they aren't.
- If one segment looks longer than another, you may not assume that it really is.
- If an angle looks like a right angle, you may not assume that it is.
- If an angle looks acute or obtuse, you may not assume that it is.
- If two angles look congruent, you may not assume that they are.
- If two angles don't look congruent, you may not ssume that they aren't.
- If two lines appear to be parallel, you may not assume that they are.
- If two lines appear to
*not*be parallel, you cannot assume that they aren't, unless their intersection point is part of the diagram.

The list below is things you *can *assume from a diagram. This list might not be universal; study your geometry text and see if this list matches the assumptions made based on diagrams in your book.

**Assumptions you can make**

- If three or more points appear to be collinear (they are connected by what appears to be a straight line), you may assume that they are collinear.
- If three points are collinear, the point which appears to be
*between*the othe two really is between them. - If a point appears to be on the interior of an angle, it really is on the interior.
- If a point appears to be on the exterior of an angle, it really is on the exterior.

Lesson by Mr. Twitchell

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