To determine which theorem proves that the two triangles are congruent based on their patterns, we need to analyze the provided options:
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SAS Theorem (Side-Angle-Side): This theorem states that if two sides of one triangle are equal to two sides of another triangle and the included angle between those sides is also equal, then the triangles are congruent.
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ASA Theorem (Angle-Side-Angle): This theorem states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.
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SSS Theorem (Side-Side-Side): This theorem states that if all three sides of one triangle are equal to the corresponding sides of another triangle, then the triangles are congruent.
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HL Theorem (Hypotenuse-Leg): This theorem is specific to right triangles. It states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Without the image, I cannot determine which theorem specifically applies to your two triangles. However, if you know the relationships between the sides and angles of the triangles (like whether they are right triangles), you can choose the correct theorem that applies.
If the triangles have:
- Two sides and the included angle equal → SAS Theorem
- Two angles and the included side equal → ASA Theorem
- All three sides equal → SSS Theorem
- If they are right triangles with the hypotenuse and one leg equal → HL Theorem
Based on that reasoning, you can select the appropriate theorem for the congruence of the triangles.
1 answer