Meridian Community College webass isosceles GMP-Module (c) Name the base angles. (Select all that apply.) \(

Ask by Estrada Riley. in the United States

Feb 04,2025

Sure, let's go through each part step-by-step based on the properties of an isosceles triangle. Assuming we have an isosceles triangle \( \triangle XYZ \) where \( XY = XZ \), here's how the angles and sides are typically labeled: - **Base Angles**: Angles opposite the equal sides. - **Vertex Angle**: The angle between the two equal sides. Given this, let's address each question: --- **(c) Name the base angles. (Select all that apply.)** **Options:** - \( \angle X \) - \( \angle Z \) - \( \angle Y \) **Answer:** - \( \angle X \) - \( \angle Z \) **Explanation:** In an isosceles triangle \( \triangle XYZ \) with \( XY = XZ \), the base angles are \( \angle X \) and \( \angle Z \), as they are opposite the equal sides. \( \angle Y \) is the vertex angle. --- **(d) Which side is opposite \( \angle X \)?** **Options:** - \( \overline{ZY} \) - \( \overline{XY} \) - \( \overline{xz} \) **Answer:** - \( \overline{ZY} \) **Explanation:** In \( \triangle XYZ \), \( \angle X \) is opposite side \( \overline{ZY} \). --- **(e) What is the vertex angle?** **Options:** - \( \angle Z \) - \( \angle \gamma \) - \( \angle X \) **Answer:** - \( \angle \gamma \) **Explanation:** Assuming \( \angle \gamma \) corresponds to \( \angle Y \) in \( \triangle XYZ \), it is the vertex angle, situated between the two equal sides \( XY \) and \( XZ \). --- **(f) Which angle is opposite side \( \overline{XY} \)?** **Options:** - \( \angle Z \) - \( \angle X \) **Answer:** - \( \angle Z \) **Explanation:** Side \( \overline{XY} \) is opposite \( \angle Z \) in \( \triangle XYZ \). --- **(g) Which two angles are congruent? (Select all that apply.)** **Options:** - \( \angle \gamma \) - \( \angle X \) - \( \angle Z \) **Answer:** - \( \angle X \) - \( \angle Z \) **Explanation:** In an isosceles triangle, the base angles are congruent. Therefore, \( \angle X \) and \( \angle Z \) are congruent. --- **Summary of Answers:** - **(c):** \( \angle X \), \( \angle Z \) - **(d):** \( \overline{ZY} \) - **(e):** \( \angle \gamma \) - **(f):** \( \angle Z \) - **(g):** \( \angle X \), \( \angle Z \) I hope this helps! If you have a specific diagram or additional information, feel free to share for more precise assistance.