In Exercises 23 and 24, supply the missing statements and reasons.
Given:  Quadrilateral PQST with midpoints A, B, C, and D of the sides  
Prove:  ABCD is a

PROOF  
Statements  Reasons 
1. Quadrilateral PQST with midpoints A, B, C, and D of the sides  1. ? 
2. Draw

2. Through two points, there is one line 
3.

3. The line joining the midpoints of two sides of a triangle is

4.

4. ? 
5.

5. ? 
6. Draw

6. ? 
7.

7. ? 
8.

8. ? 
9.

9. ? 
10. ?  10. If both pairs of opposite sides of a quadrilateral are

To supply:
The missing statements and reasons and prove ABCD is a
ASA Rule for triangle congruency:
Calculation:
Consider the quadrilateral.
The inner parallelogram creates four separate triangles. We must prove that the triangles opposite each other a congruent.
PROOF  
Statements  Reasons 
1. Quadrilateral PQST with midpoints A, B, C, and D of the sides  1. Given 
2. Draw 
2. Through two points, there is one line 
3. 
3. The line joining the midpoints of two sides of a triangle is 
4. 
4. The line joining the midpoints of two sides of a triangle is 
5. 
5 
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