Math Problem Statement
Is it possible to prove that the triangles in the given image are congruent? If so, state the postulate or theorem you would use.
Solution
Let's analyze the three triangle pairs in the image and determine if we can prove their congruence.
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Problem 3: ΔABC, ΔQRS
- We see that there are two sides marked congruent (AB = QR and AC = QS) and the angle between them (∠A = ∠Q) is also marked as congruent.
- Conclusion: The triangles are congruent by SAS (Side-Angle-Side) congruence postulate.
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Problem 4: ΔXYZ, ΔJKL
- The sides are marked as congruent (XY = JK, XZ = JL) and the included angles (∠XYZ = ∠JKL) are marked as congruent as well.
- Conclusion: The triangles are congruent by SAS (Side-Angle-Side) congruence postulate.
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Problem 5: ΔPQR, ΔRSP
- These triangles share side QR, and the other sides are marked congruent (PQ = RS and PR = RP), with corresponding angles marked congruent as well.
- Conclusion: The triangles are congruent by SSS (Side-Side-Side) congruence postulate.
Would you like further details or explanations on any of these problems?
Here are five related questions:
- What are the main criteria for triangle congruence?
- How can we prove triangles are congruent using the ASA postulate?
- Why is the SAS postulate considered a valid method for proving congruence?
- Can two triangles with the same area be congruent?
- What is the difference between congruence and similarity of triangles?
Tip: Always look for corresponding parts of triangles (angles and sides) when trying to prove congruence using different postulates.
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Math Problem Analysis
Mathematical Concepts
Triangle Congruence
Geometric Postulates
Congruence Postulates
Formulas
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Theorems
SAS (Side-Angle-Side) Congruence Postulate
SSS (Side-Side-Side) Congruence Postulate
Suitable Grade Level
Grades 8-10