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Pl3ase help me with Geometry. right angles and perpendicular angles

Pl3ase help me with Geometry. right angles and perpendicular angles-example-1
User Ashin
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1 Answer

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(Question 3)

Because of the definition of a perpendicular bisector, we know that angle B is a right angle (90°) an that


\bar{DB}=\bar{BE}

Note that AB is a segment that is shared by both triangles in the image. By using SAS (Side-Angle-Side), we can find that both the triangles are congruent (they are equal). Therefore,


\begin{gathered} 3x-9=x+21\rightarrow3x-x=21+9\rightarrow2x=30 \\ \rightarrow x=(30)/(2) \\ \rightarrow x=15 \end{gathered}

We know that


AE=x+21

We'll just have to plug in the value of x we calculated to find the lenght of AE


AE=15+21\rightarrow AE=36

Therefore, AE = 36

(Question 4)

Because of the definition of a perpendicular bisector, we know that XY splits TS right by the middle. So if TS = 10, RS would be worth half of that

Therefore, RS = 5

User Tony Borf
by
7.2k points

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