Question was provided via image upload.

Question

Accepted Answer

Let's solve these problems one by one:

### Problem 5
# Explanation:
## Step1: Identify the property
The statement shows that if $ AM = MB $, then adding 5 to both sides keeps them equal. This is the Addition Property of Equality.
# Answer:
Addition Property of Equality

### Problem 6
# Explanation:
## Step1: Identify the property
The statement $ m\angle L = m\angle L $ shows that a quantity is equal to itself, which is the Reflexive Property of Equality.
# Answer:
Reflexive Property of Equality

### Problem 7
# Explanation:
## Step1: Identify the property
Given $ m\angle A = 29^\circ $ and $ m\angle B = 29^\circ $, so $ m\angle A = m\angle B $ because they have the same measure. This is the Substitution Property (or Transitive, but here it's substituting the equal measures).
# Answer:
Substitution Property of Equality (or Transitive, but more accurately Substitution here as we substitute the equal values)

### Problem 8
# Explanation:
## Step1: Identify the property
If $ AB = LM $, then $ LM = AB $ shows that if $ a = b $, then $ b = a $, which is the Symmetric Property of Equality.
# Answer:
Symmetric Property of Equality

### Problem 9
# Explanation:
## Step1: Identify the property
If $ BC = XY $ and $ XY = 8 $, then $ BC = 8 $ by substituting $ XY $ with 8 in the first equation. This is the Transitive Property of Equality (since $ BC = XY $ and $ XY = 8 $, so $ BC = 8 $).
# Answer:
Transitive Property of Equality

### Problem 10
# Explanation:
## Step1: Identify the property
If $ m\angle Q = m\angle R $, then $ m\angle R = m\angle Q $ shows the Symmetric Property of Equality (if $ a = b $, then $ b = a $).
# Answer:
Symmetric Property of Equality

### Problem 11
# Explanation:
## Step1: Apply Substitution Property
Given $ AB = 20 $, then $ AB + CD = 20 + CD $ by substituting $ AB $ with 20.
# Answer:
$ 20 + CD $

### Problem 12
# Explanation:
## Step1: Apply Symmetric Property
If $ m\angle 1 = m\angle 2 $, then by Symmetric Property, $ m\angle 2 = m\angle 1 $.
# Answer:
$ m\angle 2 = m\angle 1 $

### Problem 13
# Explanation:
## Step1: Apply Addition Property
If $ AB = CD $, then by Addition Property of Equality, $ AB + EF = CD + EF $.
# Answer:
$ CD + EF $

### Problem 14
# Explanation:
## Step1: Apply Multiplication Property
If $ AB = CD $, then by Multiplication Property of Equality, $ 5 \cdot AB = 5 \cdot CD $.
# Answer:
$ 5 \cdot CD $

### Problem 15
# Explanation:
## Step1: Apply Subtraction Property
Subtraction Property of Equality: If $ LM = XY $, then $ LM - GH = XY - GH $.
# Answer:
$ XY - GH $

### Problem 16
# Explanation:
## Step1: Apply Distributive Property
Distributive Property: $ 5(AB + 8) = 5 \cdot AB + 5 \cdot 8 = 5AB + 40 $. So if $ 5(AB + 8) = 2 $, then $ 5AB + 40 = 2 $.
# Answer:
$ 5AB $, $ 40 $

### Problem 17
# Explanation:
## Step1: Apply Transitive Property
Transitive Property of Equality: If $ m\angle 1 = m\angle 2 $ and $ m\angle 2 = m\angle 3 $, then $ m\angle 1 = m\angle 3 $.
# Answer:
$ m\angle 1 = m\angle 3 $

### Problem 18
# Explanation:
## Step1: Apply Reflexive Property
Reflexive Property of Equality: $ m\angle ABC = m\angle ABC $.
# Answer:
$ m\angle ABC $

### Problem 19
# Explanation:
## Step1: Start with given
Given $ m\angle ABD = m\angle CBE $.
## Step2: Subtract $ m\angle 2 $ from both sides
$ m\angle ABD - m\angle 2 = m\angle CBE - m\angle 2 $ (Subtraction Property of Equality)
## Step3: Identify angles
$ m\angle ABD - m\angle 2 = m\angle 1 + m\angle 2 - m\angle 2 = m\angle 1 $
$ m\angle CBE - m\angle 2 = m\angle 2 + m\angle 3 - m\angle 2 = m\angle 3 $
## Step4: Conclude
So $ m\angle 1 = m\angle 3 $
# Answer:
By Subtraction Property of Equality, $ m\angle 1 = m\angle 3 $

### Problem 20
# Explanation:
## Step1: Start with given
Given $ AC = BD $.
## Step2: Subtract $ BC $ from both sides
$ AC - BC = BD - BC $ (Subtraction Property of Equality)
## Step3: Identify segments
$ AC - BC = AB $ and $ BD - BC = CD $
## Step4: Conclude
So $ AB = CD $
# Answer:
By Subtraction Property of Equality, $ AB = CD $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 5

Step1: Identify the property

Step1: Identify the property

Step1: Identify the property

Answer:

Problem 6