Analyzing Triangle Properties: Comparing 53° Angles and 10-13 Unit Sides

Triangle Congruence with Side-Angle-Side Comparison

Look at the triangles in the diagram.

Which of the following statements is true?

535353535353101010131313131313101010AAABBBCCCDDDEEEFFF

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the triangles in the diagram.

Which of the following statements is true?

535353535353101010131313131313101010AAABBBCCCDDDEEEFFF

2

Step-by-step solution

According to the existing data:

EF=BA=10 EF=BA=10 (Side)

ED=AC=13 ED=AC=13 (Side)

The angles equal to 53 degrees are both opposite the greater side (which is equal to 13) in both triangles.

(Angle)

Since the sides and angles are equal among congruent triangles, it can be determined that angle DEF is equal to angle BAC

3

Final Answer

Angles BAC is equal to angle DEF.

Key Points to Remember

Essential concepts to master this topic
  • SAS Congruence: Two sides and included angle determine triangle congruence
  • Technique: Match corresponding sides BA=EF=10, AC=ED=13, and angles
  • Check: Corresponding angles are equal when triangles are congruent ✓

Common Mistakes

Avoid these frequent errors
  • Assuming triangles are congruent without checking all conditions
    Don't just compare one or two measurements and conclude triangles are congruent = wrong analysis! You need to verify that corresponding sides and angles match properly. Always check that equal sides are in corresponding positions and angles are between the correct sides.

Practice Quiz

Test your knowledge with interactive questions

Look at the triangles in the diagram.

Which of the statements is true?

727272727272131313222131313222AAABBBCCCDDDEEEFFF

FAQ

Everything you need to know about this question

How do I know which angles correspond to each other?

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Look at the sides that form each angle. In triangle ABC, angle BAC is between sides BA and AC. In triangle DEF, angle DEF is between sides DE and EF. Since BA=EF=10 and AC=DE=13, these angles correspond.

Why are the 53° angles important in this problem?

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The 53° angles are opposite the longest sides in both triangles. Since ED=AC=13 (the longest sides), and both triangles have a 53° angle opposite these sides, this helps confirm the triangles have the same shape.

What does it mean for triangles to be congruent?

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Congruent triangles have exactly the same size and shape. All corresponding sides are equal and all corresponding angles are equal. They're like identical copies that might just be rotated or flipped.

Can I use just the side lengths to prove congruence?

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If you have all three sides equal (SSS), yes! But in this problem, we're also given angle measurements, so we can use Side-Angle-Side (SAS) reasoning to identify corresponding parts.

How do I identify corresponding vertices?

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Match vertices that are in similar positions. Since BA=EF=10, AC=ED=13, and both have 53° angles in corresponding positions, vertex A corresponds to vertex E, B to F, and C to D.

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