To determine which statement is incorrect, we will analyze each option step by step.
### Step 1: Analyze Statement 1
**Statement 1:** If three angles of a quadrilateral are equal, then it is always a parallelogram.
1. **Understanding the properties of a quadrilateral:** A quadrilateral has four angles, and the sum of the angles in any quadrilateral is 360 degrees.
2. **If three angles are equal:** Let’s denote the three equal angles as \( x \). Therefore, the fourth angle can be expressed as \( 360 - 3x \).
3. **Setting up the equation:** For the quadrilateral to have three equal angles, we can set \( x = 90 \) degrees. This would mean the fourth angle is \( 360 - 3(90) = 90 \) degrees.
4. **Conclusion:** If all four angles are 90 degrees, then the quadrilateral is a rectangle, which is a type of parallelogram. However, if we take \( x = 60 \) degrees, the fourth angle would be \( 360 - 3(60) = 180 \) degrees, which is not possible in a quadrilateral. Therefore, having three equal angles does not guarantee that the quadrilateral is a parallelogram.
**Result:** Statement 1 is incorrect.
### Step 2: Analyze Statement 2
**Statement 2:** The line segment joining the midpoints of the sides of an equilateral triangle divides it into four congruent triangles.
1. **Understanding the equilateral triangle:** An equilateral triangle has all sides equal and all angles equal (60 degrees each).
2. **Finding midpoints:** Let’s denote the vertices of the triangle as \( A, B, C \). The midpoints of sides \( AB, BC, \) and \( CA \) can be labeled as \( D, E, \) and \( F \) respectively.
3. **Drawing segments:** When we connect the midpoints \( D, E, \) and \( F \), we create four smaller triangles: \( \triangle ADF, \triangle DBE, \triangle ECF, \) and \( \triangle DEF \).
4. **Congruency:** By the SSS (Side-Side-Side) congruence criterion, all four triangles are congruent because they share sides that are half the lengths of the original triangle's sides.
**Result:** Statement 2 is correct.
### Step 3: Analyze Statement 3
**Statement 3:** In parallelogram PQRS, if diagonal SQ bisects angle PQR, and if angle PQR is 42 degrees, then angle SQR is 96 degrees.
1. **Understanding the properties of a parallelogram:** In a parallelogram, opposite angles are equal and consecutive angles are supplementary.
2. **Given angle:** We are given that \( \angle PQR = 42 \) degrees.
3. **Using the property of angles:** Since \( PQRS \) is a parallelogram, \( \angle PQR + \angle SQR = 180 \) degrees.
4. **Calculating angle SQR:**
\[
\angle SQR = 180 - 42 = 138 \text{ degrees}
\]
5. **Conclusion:** The statement claims that \( \angle SQR \) is 96 degrees, which contradicts our calculation.
**Result:** Statement 3 is incorrect.
### Final Conclusion
After analyzing all three statements, we find that:
- Statement 1 is incorrect.
- Statement 2 is correct.
- Statement 3 is incorrect.
Thus, the incorrect statement is **Statement 1**.
---
