Finding the Missing Statement and Reason in Step 5

Oct 13, 2025 by leolavanderia.com.br 149 views

Introduction

In geometry, proving statements is a crucial skill that helps us understand and apply mathematical concepts. Given a statement, we need to identify the missing statement and reason in a step-by-step proof. In this article, we will explore how to prove a given statement using a step-by-step approach.

The Given Statement

Given: $m \angle A D E=60^{\circ}$ and $m \angle C D F=(3 x+15)^{\circ}$

The Prove Statement

Prove: $x=15$

Step-by-Step Proof

Step	Statement	Reason
1	$m \angle A D E=60^{\circ}$	Given
2	$m \angle C D F=(3 x+15)^{\circ}$	Given
3	$m \angle A D E + m \angle C D F = 180^{\circ}$	Linear Pair Property
4	$60^{\circ} + (3 x+15)^{\circ} = 180^{\circ}$	Substitution Property
5	Missing Statement	Missing Reason
6	$3 x+75^{\circ} = 120^{\circ}$	Simplification Property
7	$3 x = 45^{\circ}$	Subtraction Property
8	$x = 15^{\circ}$	Division Property

Finding the Missing Statement and Reason in Step 5

To find the missing statement and reason in step 5, we need to analyze the previous steps and identify the relationship between the statements.

In step 4, we have the equation $60^{\circ} + (3 x+15)^{\circ} = 180^{\circ}$ . To simplify this equation, we need to combine like terms.

Using the Distributive Property, we can rewrite the equation as:

$60^{\circ} + 3 x^{\circ} + 15^{\circ} = 180^{\circ}$

Now, we can combine the constant terms:

$75^{\circ} + 3 x^{\circ} = 180^{\circ}$

This is the missing statement in step 5. The missing reason is the Simplification Property, which allows us to combine like terms.

Conclusion

In this article, we have explored how to prove a given statement using a step-by-step approach. We have identified the missing statement and reason in step 5 and analyzed the relationship between the statements. By following this approach, we can prove geometric statements and understand the underlying mathematical concepts.

Key Takeaways

To prove a statement, we need to identify the missing statement and reason in a step-by-step proof.
The Linear Pair Property states that the sum of the measures of two adjacent angles is $180^{\circ}$ .
The Substitution Property allows us to replace a variable with a value.
The Simplification Property allows us to combine like terms.
The Distributive Property allows us to distribute a coefficient to multiple terms.

Q: What is a geometric statement?

A: A geometric statement is a mathematical statement that involves geometric shapes and their properties. It can be a statement about the size, shape, or position of a geometric figure.

Q: What is the purpose of proving a geometric statement?

A: The purpose of proving a geometric statement is to demonstrate that the statement is true using logical and mathematical reasoning. This helps to establish the validity of the statement and provides a deeper understanding of the underlying mathematical concepts.

Q: What are the key steps in proving a geometric statement?

A: The key steps in proving a geometric statement are:

Identify the given information: Identify the given statements and any relevant information.
Determine the goal: Determine what needs to be proven.
Develop a plan: Develop a plan for the proof, including the steps to take and the reasoning to use.
Execute the plan: Execute the plan, using logical and mathematical reasoning to support each step.
Verify the conclusion: Verify that the conclusion follows logically from the previous steps.

Q: What are some common geometric properties used in proofs?

A: Some common geometric properties used in proofs include:

Linear Pair Property: The sum of the measures of two adjacent angles is $180^{\circ}$ .
Substitution Property: A variable can be replaced with a value.
Simplification Property: Like terms can be combined.
Distributive Property: A coefficient can be distributed to multiple terms.

Q: How do I know if a proof is correct?

A: To determine if a proof is correct, follow these steps:

Read the proof carefully: Read the proof carefully, paying attention to each step and the reasoning used.
Check the logic: Check the logic of each step, making sure that it follows from the previous step.
Verify the conclusion: Verify that the conclusion follows logically from the previous steps.
Check for errors: Check for errors in the proof, such as incorrect assumptions or flawed reasoning.

Q: What are some common mistakes to avoid in geometric proofs?

A: Some common mistakes to avoid in geometric proofs include:

Incorrect assumptions: Make sure that all assumptions are correct and relevant to the proof.
Flawed reasoning: Make sure that the reasoning used is logical and sound.
Incorrect conclusions: Make sure that the conclusion follows logically from the previous steps.
Omitted steps: Make sure that all necessary steps are included in the proof.

Q: How can I practice proving geometric statements?

A: To practice proving geometric statements, try the following:

Work through examples: Work through examples of geometric proofs, following the steps outlined above.
Practice with different types of proofs: Practice with different types of proofs, such as direct proofs, indirect proofs, and proof by contradiction.
Join a study group: Join a study group or find a study partner to work through geometric proofs together.
Seek help when needed: Seek help when needed, whether from a teacher, tutor, or classmate.

By following these tips and practicing regularly, you can improve your skills in proving geometric statements and become more confident in your mathematical abilities.