The very first letter in the name of a ray constantly refers come the endpoint the the ray. Therefore,

*
 has that endpoint at 
*
 and 
*
 has the endpoint at 
*
. The two rays room not opposite rays.

You are watching: Name a pair of opposite rays



Refer come the over figure. 

True or false: 

*
 and 
*
 comprise a pair of opposite rays.


Explanation:

The first letter in the name of a ray describes its endpoint; the second refers come the name of any kind of other allude on the ray. 

*
 and 
*
 are rays that have endpoint 
*
 and happen through 
*
 and , respectively. Those rays room indicated listed below in red and also green, respectively.

*

As it transforms out, the 2 rays space one and also the same.



Refer come the over figure. 

True or false: 

*
 and 
*
 comprise a pair of the contrary rays.


Explanation:

 

Two rays are opposite rays, by definition, if 

(1) they have the exact same endpoint, and

(2) your union is a line.

The first letter in the name of a ray refers to its endpoint; the 2nd refers to the surname of any other point on the ray. 

*
 and 
*
 both have endpoint 
*
, therefore the an initial criterion is met. 
*
 passes through point  and 
*
 passes with point 
*
*
 and 
*
 are indicated listed below in green and red, respectively:

*

The union that the two rays is a line. Both criteria are met, therefore the rays are certainly opposite.


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Example inquiry #1544 : an easy Geometry



Refer come the over diagram.

True or false: 

*
*
, and  are collinear points.


Possible Answers:

True


False


Correct answer:

False


Explanation:

Three points space collinear if over there is a solitary line that passes v all three. In the diagram below, it deserve to be checked out that the line the passes through 

*
 and 
*
 does not pass through 
*
.

 

*

 

Therefore, the 3 points are not collinear.


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Example inquiry #1545 : an easy Geometry


Refer come the over diagram. 

True or false: 

*
, , and 
*
 are collinear points.


Possible Answers:

True


False


Correct answer:

True


Explanation:

Three points room collinear if over there is a solitary line the passes through all three. In the chart below, it can be viewed that together a heat exists.


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Example concern #1546 : simple Geometry


True or false: The plane containing the above figure have the right to be dubbed Plane 

*
.


Possible Answers:

False


True


Correct answer:

True


Explanation:

A plane can be named after any type of three clues on the airplane that room not top top the same line. 

*
*
, and 
*
 do not show up on the same line; for example, as have the right to be seen below, the line the passes through 
*
 and 
*
 does no pass through 
*
.

Plane 

*
 is a valid name for the aircraft that has this figure.


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Example inquiry #1541 : aircraft Geometry


Refer come the over diagram. 

True or false: Quadrilateral 

*
 can likewise be called Quadrilateral 
*
.


Possible Answers:

True


False


Correct answer:

False


Explanation:

A square is named after its four vertices in consecutive order, walking clockwise or counterclockwise. Quadrilateral 

*
 is the number in red, below:

*

*
*
*
, and 
*
 are no a clockwise or counterclockwise notified of the vertices, therefore Quadrilateral 
*
 is no a valid surname for the quadrilateral.


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Example question #1548 : straightforward Geometry


Refer come the over diagram:

True or false: 

*
 may additionally called 
*
.


Possible Answers:

False


True


Correct answer:

False


Explanation:

A line deserve to be named after any two points it overcome through. The line 

*
 is indicated in environment-friendly below.

*

The line does not pass through 

*
, so 
*
 cannot be part of the name of the line. Specifically, 
*
 is not a valid name.


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Example concern #1549 : basic Geometry


Examine the diagram. I m sorry of these conditions does not prove that  

*
 ?


Possible Answers:

*
 and 
*
 


Any of these statements can be offered to prove that 

*
.


Correct answer:

*


Explanation:

If 

*
 and 
*
 , then 
*
, because two present parallel to the same line space parallel to each other.

If

*
, climate
*
, because two same-side inner angles created by transversal 
*
 are supplementary.

If 

*
, then 
*
, due to the fact that two alternative interior angles created by transversal 
*
 are congruent.

However, 

*
 regardless that whether 
*
 and 
*
 are parallel; they room vertical angles, and also by the Vertical angles Theorem, they must be congruent.


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Example question #1 : how To uncover An angle Of A line


An isosceles triangle has an inner angle the measures 

*
. What are the measures of its various other two angles?


Possible Answers:

This triangle cannot exist.


Correct answer:

 

*


Explanation:

By the Isosceles Triangle Theorem, two interior angles have to be congruent. However, since a triangle cannot have actually two obtuse inner angles, the two lacking angles must be the persons that are congruent. Because the total angle measure of a triangle is 

*
 , every of the absent angles steps
*
.


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