Question

Pl3ase help me with Geometry. right angles and perpendicular angles

Answer 1

(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