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

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Sure, let's go through each part step-by-step based on the properties of an isosceles triangle.

Assuming we have an isosceles triangle $$ 	riangle XYZ $$ 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:

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**(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 $$ 	riangle XYZ $$ 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.

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**(d) Which side is opposite $$ \angle X $$?**

**Options:**
- $$ \overline{ZY} $$
- $$ \overline{XY} $$
- $$ \overline{xz} $$

**Answer:**
- $$ \overline{ZY} $$

**Explanation:**  
In $$ 	riangle XYZ $$, $$ \angle X $$ is opposite side $$ \overline{ZY} $$.

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**(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 $$ 	riangle XYZ $$, it is the vertex angle, situated between the two equal sides $$ XY $$ and $$ XZ $$.

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**(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 $$ 	riangle XYZ $$.

---

**(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.

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**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.
**(c) Base angles:** - $$ \angle X $$ - $$ \angle Z $$ **(d) Side opposite $$ \angle X $$:** - $$ \overline{ZY} $$ **(e) Vertex angle:** - $$ \angle \gamma $$ **(f) Angle opposite side $$ \overline{XY} $$:** - $$ \angle Z $$ **(g) Congruent angles:** - $$ \angle X $$ - $$ \angle Z $$

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

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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