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.

True

False

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.

True

False

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

.

False

True

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

False

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:

.

False

True

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

?

and

Any of these statements can be offered to prove that

.

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?

This triangle cannot exist.

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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