To determine which theorem proves that the two triangles are congruent, we need to consider the specific information available about the sides and angles of the triangles.
Here's a brief overview of the congruence theorems:
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SSS (Side-Side-Side) Theorem: If all three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.
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SAS (Side-Angle-Side) Theorem: If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
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ASA (Angle-Side-Angle) Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
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AAS (Angle-Angle-Side) Theorem: If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
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HL (Hypotenuse-Leg) Theorem: This theorem is specific to right triangles. If the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.
Without seeing the image of the triangles, I cannot definitively determine which theorem applies. However, if the triangles are congruent based on either all sides being equal or a combination of sides and angles, you could use SSS or SAS, depending on the information given.
If the triangles are right triangles and you know the lengths of the hypotenuse and one leg, then HL would be the applicable theorem.
Please provide more details about the triangles (sides and angles) so I can help you choose the correct theorem!
5 answers