Triangle Congruence: Finding Missing Data in Triangles ABC and DEF with 41° and 39° Angles

Triangle Congruence with Non-Matching Angles

What data must be added so that the triangles are congruent?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What data must be added so that the triangles are congruent?

414141393939777999999777AAABBBCCCDDDEEEFFF

2

Step-by-step solution

It is not possible to add data for the triangles to be congruent since the corresponding angles are not equal to each other and therefore the triangles could not be congruent to each other.

3

Final Answer

Data cannot be added for the triangles to be congruent.

Key Points to Remember

Essential concepts to master this topic
  • Angle Rule: Corresponding angles must be equal for congruent triangles
  • Analysis: Triangle ABC has angles 41° and 39°, DEF doesn't match
  • Check: Compare all corresponding angle pairs - if any differ, triangles cannot be congruent ✓

Common Mistakes

Avoid these frequent errors
  • Assuming matching side lengths guarantee congruence
    Don't focus only on matching sides like AB=7=EF and AC=9=DF = triangle congruence! Even with matching sides, if corresponding angles don't match (41° vs different angles), triangles cannot be congruent. Always check that ALL corresponding angles are equal first.

Practice Quiz

Test your knowledge with interactive questions

Look at the triangles in the diagram.

Which of the statements is true?

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FAQ

Everything you need to know about this question

Why can't I just make the angles match by adding data?

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You cannot change the given angles in a triangle! Triangle ABC already has angles of 41° and 39°, and triangle DEF has a 39° angle in a different position. The sum of angles must equal 180°, so changing one angle changes the whole triangle.

What if I match all the side lengths - won't that work?

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No! Even with matching sides, triangles need matching corresponding angles to be congruent. These triangles have different angle arrangements, so they cannot be congruent regardless of side lengths.

How do I know which angles correspond to each other?

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Corresponding angles are in the same relative position. In triangle ABC, angle A is opposite side BC. In triangle DEF, angle D should be opposite the corresponding side EF. Check if these angles match!

Could these triangles be similar instead of congruent?

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Possibly! Similar triangles have the same angles but different sizes. However, from the given information, we can see the angles don't match in the correct positions, so these triangles are likely neither congruent nor similar.

What would I need to make triangles congruent?

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You would need completely different triangles where all corresponding angles match exactly. Since you cannot change the given angle measurements, these specific triangles cannot be made congruent.

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