How are the three rock samples similar and different from each other?

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1. **Composition and Mineral Content**  
   - All rock samples are made up of minerals and are part of the solid Earth. Their constituent minerals determine properties such as color, hardness, and density.  
   - For example, if you have a rock rich in quartz, you might note that its composition includes a high percentage of $$ \text{SiO}_2 $$ (silicon dioxide).

2. **Formation Processes**  
   - **Igneous Rocks:** Formed by the cooling and solidification of magma or lava. Their textures can range from coarse-grained (when cooled slowly underground) to fine-grained (when cooled quickly at the surface).  
   - **Sedimentary Rocks:** Formed by the deposition, compaction, and cementation of sediments. They often exhibit layers and may contain fossils.  
   - **Metamorphic Rocks:** Formed by the alteration of existing rock (igneous, sedimentary, or another metamorphic rock) due to heat, pressure, or chemically active fluids. Their textures can show foliation or banding caused by the reorientation of minerals under stress.

3. **Textures and Structures**  
   - **Similarities:**  
     - Despite different origins, each rock sample will show a mineral grain size and structure that reflects its history.  
     - They may all display features such as grain boundaries or embedded minerals.  
   - **Differences:**  
     - An igneous rock might have interlocking crystals indicating slow or rapid cooling.  
     - A sedimentary rock often has a layered structure (stratification) and may include rounded grains or fossils.  
     - A metamorphic rock can have a foliated structure with aligned mineral grains, revealing the direction of pressure during formation.

4. **Role in the Rock Cycle**  
   - All three types are interconnected within the rock cycle. For instance, an igneous rock can be weathered to form sediments, which then lithify into a sedimentary rock. Under pressure and heat, that sedimentary rock can metamorphose into a metamorphic rock.  
   - This cycle can be conceptually represented as:  
     $$
     \text{Igneous} \rightarrow \text{Weathering/Deposition} \rightarrow \text{Sedimentary} \rightarrow \text{Metamorphism} \rightarrow \text{Metamorphic}
     $$
     
5. **Key Similarities and Differences Summarized**  
   - **Similarities:**  
     - All are composed of minerals, and their characteristics (such as hardness, color, and grain size) are determined by mineral content.  
     - Each plays a role in Earth’s dynamic rock cycle.  
   - **Differences:**  
     - **Origin:** Igneous rocks form from cooling magma, sedimentary rocks from deposition of materials, and metamorphic rocks from the alteration of pre-existing rocks.  
     - **Texture:** The processes give rise to distinct textures—interlocking crystals in igneous rocks, layering in sedimentary rocks, and foliation or banding in metamorphic rocks.  
     - **Environmental History:** The conditions of formation (such as cooling rate, pressure, and temperature) impart unique characteristics to each rock sample.

By comparing these aspects, you can identify both the commonalities (mineral composition, role in the rock cycle) and differences (formation process, texture, structure) among the three rock samples.
All three rock samples are made of minerals and play roles in the rock cycle. They share similar mineral compositions and textures influenced by their formation. However, they differ in how they were formed: igneous rocks come from cooling magma, sedimentary rocks from deposited materials, and metamorphic rocks from altered existing rocks. Their textures also vary—igneous rocks have interlocking crystals, sedimentary rocks have layered structures, and metamorphic rocks show foliated patterns.

How are the three rock samples similar and different from each other?

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