Construct a triangle PQR such that PQ = QR = 4 . 7 cm and `angle Q = 72^(@)` . Measure angles P and R . Name the triangle

Answer

### Step-by-Step Solution:

1. **Draw Line Segment PQ:**
- Begin by drawing a line segment PQ that measures 4.7 cm. Use a ruler for accuracy.
- Label the endpoints as P and Q.

**Hint:** Use a ruler to measure exactly 4.7 cm for the line segment.

2. **Construct Angle Q:**
- Place a protractor at point Q.
- Measure and mark an angle of 72 degrees from line segment PQ.
- Draw a ray from Q at this angle; label the point where this ray intersects as R.

**Hint:** Ensure the protractor is aligned correctly with PQ to measure the angle accurately.

3. **Draw Line Segment QR:**
- Using a compass, set the width to 4.7 cm (the length of QR).
- With the compass point on Q, draw an arc that intersects the ray you drew from Q. Label the intersection point as R.

**Hint:** Make sure the compass is opened to exactly 4.7 cm before drawing the arc.

4. **Complete Triangle PQR:**
- Connect points P and R with a straight line to complete triangle PQR.

**Hint:** Use a ruler to ensure that line PR is straight.

5. **Measure Angles P and R:**
- Use the protractor to measure angle P (the angle at point P) and angle R (the angle at point R).
- Record the measurements.

**Hint:** Place the protractor carefully at point P and R to get accurate angle readings.

6. **Identify the Triangle:**
- Since PQ = QR and angles P and R are equal, triangle PQR is an isosceles triangle.

**Hint:** Remember that in an isosceles triangle, two sides are equal, and the angles opposite those sides are also equal.

### Final Naming:
- Name the triangle as Triangle PQR, which is an isosceles triangle.

### Summary of Measurements:
- PQ = QR = 4.7 cm
- Angle Q = 72 degrees
- Angles P and R are both measured to be 54 degrees each.