construct a triangle XYZ in which XY=6.5cm,XZ=5.7cm and <XYZ=58degrees.

To construct triangle XYZ where \( XY = 6.5 \, \text{cm} \), \( XZ = 5.7 \, \text{cm} \), and \( \angle XYZ = 58^\circ \), follow these steps:

### Materials needed:
- A ruler
- A protractor
- A compass
- A pencil

### Steps:

1. **Draw Line Segment XY:**
   - Using the ruler, draw a line segment \( XY \) of length \( 6.5 \, \text{cm} \).

2. **Mark the Angle \( \angle XYZ \):**
   - Place the protractor on point \( Y \) with the baseline along \( XY \).
   - Measure and mark an angle of \( 58^\circ \) from \( XY \), creating the angle \( \angle XYZ \).

3. **Draw Ray for Side XZ:**
   - From point \( Y \), draw a ray along the direction of the \( 58^\circ \) angle.

4. **Mark the Length of XZ:**
   - Set the compass to a radius of \( 5.7 \, \text{cm} \) (length of \( XZ \)).
   - Place the compass point on \( X \), and draw an arc that intersects the ray from step 3. Label the intersection point as \( Z \).

5. **Complete the Triangle:**
   - Now, connect points \( Z \) and \( Y \) with a straight line.

You have now constructed triangle XYZ with the given dimensions.

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Do you want further details or explanations on the steps? 

### 5 Related Questions:
1. How do you verify if your constructed triangle is accurate?
2. How can you construct the bisector of angle \( XYZ \)?
3. What would change if \( \angle XYZ \) were larger or smaller?
4. How can you calculate the area of triangle XYZ with these given dimensions?
5. What properties of triangle XYZ can be deduced based on these lengths and angle?

### Tip:
When drawing angles, ensure the protractor's baseline is perfectly aligned with the drawn line segment to avoid errors.

Construct a triangle XYZ in which XY=6.5cm, XZ=5.7cm, and ∠XYZ=58°.

Learn how to construct triangle XYZ where XY=6.5cm, XZ=5.7cm, and ∠XYZ=58°. This step-by-step guide involves basic geometry concepts and is suitable for students in Grades 6-8.

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