Congruent Triangles ABO and CBO: Finding Equal Side to BC

Triangle Congruence with Corresponding Vertices

The triangles ABO and CBO are congruent.

Which side is equal to BC?

AAABBBCCCDDDOOO

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 In congruent triangles, which side matches with side B C?
00:11 Let's explore all the matching sides step by step.
00:33 And that's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The triangles ABO and CBO are congruent.

Which side is equal to BC?

AAABBBCCCDDDOOO

2

Step-by-step solution

Let's consider the corresponding congruent triangles letters:

CBO=ABO CBO=ABO

That is, from this we can determine:

CB=AB CB=AB

BO=BO BO=BO

CO=AO CO=AO

3

Final Answer

Side AB

Key Points to Remember

Essential concepts to master this topic
  • Congruence Rule: Congruent triangles have equal corresponding sides and angles
  • Technique: Match vertex order: triangle CBO corresponds to triangle ABO
  • Check: Verify corresponding sides match: CB = AB, BO = BO, CO = AO ✓

Common Mistakes

Avoid these frequent errors
  • Matching sides randomly without considering vertex order
    Don't assume BC equals any random side from triangle ABO = wrong correspondence! The vertex order CBO → ABO is crucial for finding correct pairs. Always match sides by following the exact vertex order given in the congruence statement.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the triangles DCE and ABE congruent?

If so, according to which congruence theorem?

AAABBBCCCDDDEEE50º50º

FAQ

Everything you need to know about this question

How do I know which sides correspond to each other?

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Look at the order of vertices in the congruence statement! Triangle CBO ≅ Triangle ABO means C matches A, B matches B, and O matches O. So side CB corresponds to side AB.

Why does the order of letters matter in congruent triangles?

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The order tells you which vertices match! The first letter in each triangle name corresponds, the second letters correspond, and so on. This is how we identify equal sides and angles.

What if I write the congruence statement differently?

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You can write it differently, but the corresponding order must stay the same. For example, ABO ≅ CBO means A↔C, B↔B, O↔O, so AB = CB, which is the same as BC = AB.

Are all sides in congruent triangles equal?

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No! Only corresponding sides are equal. In triangle ABO ≅ triangle CBO, we have AB = CB, AO = CO, and BO = BO, but AB doesn't equal AO.

How can I remember which sides correspond?

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Use the vertex matching method: Write the triangles with matching vertices lined up vertically. Triangle CBO over triangle ABO shows C↔A, B↔B, O↔O clearly!

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