a. name the vertex of <4 b. Name the sides of <1 c. Write another Name for <5 d. classify each angle

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Question:

13.) Write a Paragraph proof ( Thanks!!)

Given Line BC = Line EC and Line AC = DC Line
Prove Line BA= Line ED

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Answer:

An angle is an undefined term in plane geometry.

  • The vertex of ?f=%5Cangle%204 is B
  • The sides of ?f=%5Cangle%201 are BC and BD
  • Another name for ?f=%5Cangle%205 is ?f=%5Cangle%20DBE.
  • ?f=%5Cangle%20FBC is a right angle
  • ?f=%5Cangle%20EBF is an obtuse angle
  • ?f=%5Cangle%20ABC is a straight angle.
  • ?f=%5Cangle%20EBC%20%3D%20144
  • ?f=%5Cangle%20ABE%20%3D13

Vertex of ?f=%5Cangle%204

The vertex of an angle is the point where the rays that form the angle meet.

From the diagram, rays BE and BA meet at point B to form ?f=%5Cangle%204.

Hence, the name of the vertex is B

Sides of ?f=%5Cangle%201

The sides of an angle are the rays or sides that form the angle

?f=%5Cangle%201 is formed by rays BC and BD

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Hence, the sides are BC and BD

Another name for ?f=%5Cangle%205

An angle can be named by combining the sides and the vertex.

The sides of ?f=%5Cangle%205 are DB and BE, while the vertex is B

This means that rays DB and BE meet at point B

Hence, another name is ?f=%5Cangle%20DBE

Classify the angles

Angles are classified based on the measure

?f=%5Cangle%20FBC is a right angle, because ?f=%5Cangle%20FBC%20%3D%2090%5Eo

?f=%5Cangle%20EBF is an obtuse angle because ?f=%5Cangle%20EBF is greater than ?f=90%5Eo but less than ?f=180%5Eo

?f=%5Cangle%20ABC is a straight angle, because ?f=%5Cangle%20ABC%3D%20180%5Eo

Angle bisector

The line or ray that divides an angle into equal halves is an angle bisector.

Ray BE is an angle bisector, because it divides ?f=%5Cangle%20DBA into two equal halves.

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Find ?f=%5Cangle%20EBC

We have:

?f=%5Cangle%20EBD%20%3D%2036

?f=%5Cangle%20DBC%20%3D%20108

?f=%5Cangle%20EBC is calculated using:

?f=%5Cangle%20EBC%20%3D%20%5Cangle%20EBD%20%2B%5Cangle%20DBC

?f=%5Cangle%20EBC%20%3D%20108%2B36

?f=%5Cangle%20EBC%20%3D%20144

Find ?f=%5Cangle%20ABE

?f=%5Cangle%20EBF%20%3D%20117

?f=%5Cangle%20ABE is calculated using:

?f=%5Cangle%20EBF%20%3D%20%5Cangle%20ABE%20%2B%5Cangle%20EBD%20%2B%20%5Cangle%20ABF

Where

?f=%5Cangle%20ABF%20%3D%2090

?f=%5Cangle%20ABE%20%3D%20%5Cangle%20EBD

So, we have:

?f=117%20%3D%20%5Cangle%20ABE%20%2B%5Cangle%20ABE%20%2B%20%5Cangle%2090

?f=117%20%3D%202%5Cangle%20ABE%20%2B%2090

Collect like terms

?f=2%5Cangle%20ABE%20%3D117%20 %2090

?f=2%5Cangle%20ABE%20%3D27

Divide both sides by 2

?f=%5Cangle%20ABE%20%3D13

Read more about angles at:

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