https://file.aiquickdraw.com/mathbot/file/17278167935557qss2ydk.jpg

Let's go over the problems on the uploaded quiz.

### For the first section:

You need to match each statement with the correct property, definition, or postulate from the given list.

1. **QR = QR**: This is an example of the **Reflexive Property** (F).
2. **If AB = CD, then AB + EF = CD + EF**: This is the **Addition Property of Equality** (A).
3. **If RS + TU = XY and TU = WV, then RS + WV = XY**: This is the **Substitution Property** (E).
4. **JK ≅ LM, then JK = LM**: This represents **Definition of Congruence** (I).
5. **If AB ≅ BC and BC ≅ CE, then AB ≅ CE**: This is the **Transitive Property** (G).
6. **If 2XY = YZ, then XY = ½YZ**: This is the **Division Property of Equality** (D).
7. **If Q is between P and R, then PQ + QR = PR**: This represents the **Segment Addition Postulate** (K).
8. **If 2KL = KL + MN, then KL = MN**: This is an example of the **Subtraction Property of Equality** (B).

---

### For the second part: Complete the proofs

#### Problem 9
- **Given**: \( B \) is the midpoint of \( AC \), \( AB \cong CD \)
- **Prove**: \( C \) is the midpoint of \( BD \)

Let’s fill in the proof statements:

1. \( B \) is the midpoint of \( AC \) – **Given**.
2. \( AB = BC \) – This follows from the **Definition of Midpoint** (J).
3. \( AB \cong CD \) – **Given**.
4. \( AB = CD \) – Use the **Definition of Congruence** (I) to go from congruent segments to equal segments.
5. \( BC = CD \) – Use **Substitution** to substitute \( AB \) with \( CD \).
6. \( C \) is the midpoint of \( BD \) – This follows from the **Definition of Midpoint** (J), since \( BC = CD \).

---

#### Problem 10
- **Given**: \( PS = RT \), \( PQ = ST \)
- **Prove**: \( QS = RS \)

Proof statements:

1. \( PS = RT, PQ = ST \) – **Given**.
2. \( PQ + QS = PS \) – Use the **Segment Addition Postulate** (K) for segment \( PQ + QS \).
3. \( ST + QS = RT \) – Use **Segment Addition Postulate** (K) again, this time for \( ST + QS \).
4. \( RS + ST = RT \) – Apply **Substitution** (E) to relate the segments.
5. \( ST + QS = RS + ST \) – **Transitive Property** (G), since \( PS = RT \).
6. \( QS = RS \) – Finally, subtract \( ST \) from both sides using the **Subtraction Property of Equality** (B).

---

Would you like any further details or clarification on any of these steps?

### 5 Related Questions
1. What is the reflexive property and how is it used in geometry?
2. How do you use the definition of congruence in proofs?
3. Can you explain the transitive property with more examples?
4. How does the midpoint definition help in proving congruence between segments?
5. What is the importance of the segment addition postulate in geometry?

### Tip:
When solving proofs, always start by identifying given information, then build from definitions and properties to justify each step logically.

Complete the proofs and match the segment and angle proof statements to the correct property, definition, or postulate.

Learn how to match geometric statements with their corresponding properties, definitions, or postulates, and complete proofs involving midpoint, congruence, and segment addition. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation