Bot GPT 4-o mini To prove that triangles ΔABR and ΔACR are congruent, you can use the following three congruence theorems based on the provided information:
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HL (Hypotenuse-Leg): Since triangles ABR and ACR share the side AR and both have right angles (angles ABR and ACR), you can apply the HL theorem. You also have the hypotenuse (AB for triangle ABR and AC for triangle ACR) and one leg (AR) congruent.
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SSS (Side-Side-Side): If you establish that sides AB and AC are congruent, AR is congruent to itself (shared side), and BR is congruent to CR, you can apply the SSS theorem.
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ASA (Angle-Side-Angle): Since angles ABR and ACR are both right angles, they are congruent. If you also have the sides AR being common and one of the sides (AB = AC), then you can use the ASA theorem.
So the selected options would be:
- HL
- SSS
- ASA
However, please choose only three. Based on the strongest proof, I would recommend HL, SSS, and ASA depending on the established congruencies of the angles and sides in your context. If you have strong evidence for AB = AC and BR = CR, SSS would be a strong choice. If focusing on angles, HL is a pivotal theorem for right triangles.
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