Triangle Geometry: Verifying Line Segment DE's Position in Multiple Triangles

Q: How do I identify all the triangles in a complex diagram?

Look for closed shapes with exactly three vertices. In this diagram, you have triangle ABC (the large one), plus smaller triangles ABD, BEC, and DBE formed by the internal lines.

Q: What's the difference between a line segment and a triangle side?

A triangle side must connect two vertices of the same triangle directly. Line segment DE exists in the diagram but doesn't connect vertices of any single triangle - it's part of the longer side BE.

Q: How do I systematically check each triangle?

List each triangle's three sides:Triangle ABC: AB, BC, CATriangle ABD: AB, BD, DATriangle BEC: BE, EC, CBTriangle DBE: DB, BE, EDNotice DE doesn't appear in any list!

Q: Why isn't DE a side of triangle DBE?

Triangle DBE has sides DB, BE, and ED - not DE. The side is ED (from E to D), which is the same line segment as DE but written in the standard vertex order for that triangle.

Triangle Side Identification with Line Segments

True or false:

DE not a side in any of the triangles.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether DE is a side in one of the following triangles

00:04 This can be verified using the triangles' letters

00:11 Examine each triangle to check whether DE is inside

00:22 It is not present in ABD

00:25 It is not present DBC

00:34 It is not present in ABC

00:42 It is not present in any of the triangles. This is the solution to the question.

Step-by-step written solution

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Understand the problem

True or false:

DE not a side in any of the triangles.

Step-by-step solution

To solve the problem of determining whether DE is not a side in any of the triangles, we will methodically identify the triangles present in the diagram and examine their sides:

Identify triangles in the diagram. The diagram presented forms a right-angled triangle ABC with additional lines forming smaller triangles within.
Triangles formed: Triangle ABC (major triangle), Triangle ABD, Triangle BEC, and Triangle DBE.
Let's examine the sides of these triangles:

Triangle ABC has sides AB, BC, and CA.
Triangle ABD has sides AB, BD, and DA.
Triangle BEC has sides BE, EC, and CB.
Triangle DBE has sides DB, BE, and ED.

Notice that while point D is used, the segment DE is only part of line BE and isn't listed as a direct side of any triangle.

Therefore, the claim that DE is not a side in any of the triangles is indeed correct.

Hence, the answer is True.

Final Answer

True

Key Points to Remember

Essential concepts to master this topic

Definition: Triangle sides connect vertices directly without intermediate points
Technique: List all triangles first: ABC, ABD, BEC, DBE
Check: Verify DE appears in any triangle's three sides list ✓

Common Mistakes

Avoid these frequent errors

Assuming all line segments are triangle sides
Don't assume every line segment DE automatically becomes a triangle side = wrong identification! Line segments can exist within triangles without being actual sides. Always check if the segment connects two vertices of the same triangle directly.

Practice Quiz

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Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

How do I identify all the triangles in a complex diagram?

Look for closed shapes with exactly three vertices. In this diagram, you have triangle ABC (the large one), plus smaller triangles ABD, BEC, and DBE formed by the internal lines.

What's the difference between a line segment and a triangle side?

A triangle side must connect two vertices of the same triangle directly. Line segment DE exists in the diagram but doesn't connect vertices of any single triangle - it's part of the longer side BE.

Can a line segment be part of multiple triangles?

Yes! For example, side AB is shared by both triangles ABC and ABD. But DE isn't a side of any triangle - it's just a portion of segment BE.

How do I systematically check each triangle?

List each triangle's three sides:

Triangle ABC: AB, BC, CA
Triangle ABD: AB, BD, DA
Triangle BEC: BE, EC, CB
Triangle DBE: DB, BE, ED

Notice DE doesn't appear in any list!

Why isn't DE a side of triangle DBE?

Triangle DBE has sides DB, BE, and ED - not DE. The side is ED (from E to D), which is the same line segment as DE but written in the standard vertex order for that triangle.

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