Question

Damien wrote the following statements:

Statement 1: An angle has two rays with a common endpoint.

Statement 2: If two lines intersect in one point, then exactly one plane contains both lines.

Which geometry term does each statement represent? (2 points)
Hint, use the multiple choice options to your benefit. First ask yourself, if one of the above statements is a definition.

Statement 1: definition; Statement 2: theorem
Statement 1: postulate; Statement 2: theorem
Statement 1: theorem; Statement 2: postulate
Statement 1: theorem; Statement 2: definition.

Answer 1

Explanation:

First of all, let's take a look on different terms used in Euclidean geometry:

• Definition : We use it to define something or describe about how it should look like? etc.

• Axioms : They are the basic assumptions that are given and they don't need any proof. They are obvious universal truths.

• Postulates : The axioms and assumptions linked with geometry are universal truths.

• Theoram : The propositions which were proved to verify that they were true. They were proved using definitions and axioms.

Back to Question:

In this question, we need to state the type of statements given according to the Euclidean geometry.

Given options,

• Statement 1: This is saying about a angle that how it should be or how it looks. And they are pre-defined in nature. So, this is Definition.

• Statement 2: This is also a truth, additionally it can be proven and verified by using the previous axioms and postulates. So, this is a Theoram.

Hence, the correct option is:

$\large{ \boxed{ \bf{ \purple{Option \: A}}}}$

And we are done !!

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Answer 2

Before moving to Question,

We'll understand our 'Topic'.

Here we'll take a look at some statement/terms used in Euclid's Geometry....!

• Definition:-

Something like a sentence or a word which is used to describe something.

• Axiom:-

An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.

• Theorm:-

Theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems.

So to our Question:-

Statement 1:-

An angle has two rays with a common endpoint.

• Here we will see that it's showing something that is like Definition.
• Can be said as Definition of 'Angle'

Statement 2:-

If two lines intersect in one point, then exactly one plane contains both lines.

• Here we are simply able to see that it is a Theorm.

So to our Answer:-

$\red{ \boxed{Answer=Option 'A'}}$