The perpendicular bisectors of two sides of a triangle meet at point that belongs to the third side. prove that this is a right triangle.

Statement : If the perpendicular bisectors of two sides of a triangle meet at point that belongs to the third side then this is a right angle triangle.

Prove:

Let ABC is triangle,

In which DF and EF are the perpendicular bisectors of legs AB and BC respectively.

That is, ∠ FDB = ∠BEF=  90°

Where,

Then By the property of the circumcenter,

F must be mid point of leg AC.

That is, DF ║ BC

⇒  ∠ FDB + ∠ DBC = 180° ( the sum of two adjacent angles on the parallel lines by the same transversal is supplementary )

But,  ∠ FDB = 90°

⇒∠ DBC = 90°

⇒ ∠ ABC = 90°

That is, Δ ABC is a right angle triangle.

10x

step-by-step explanation:

the greatest common factor 30 and 20 is 10

5 is a common factor of 30 and 20 but 10 is also a factor and 10 is greater than 5 so 5 will definitely not be apart of our answer

now the most amount of x's you factor our is just 1 factor of 1

so 10x the gcf of the terms in the polynomial

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

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