Answer:
See Below.
Step-by-step explanation:
In the given figure, AP = BP = PC.
And we want to prove that ∠ABC is a right angle.
Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.
By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be <em>x°</em>.
Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.
And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to <em>x°.</em>
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And since the sum of the interior angles of a triangle total 180°, we acquire:
Since they are all equivalent:
Hence:
∠ABC is the sum of ∠PBA and ∠PBC, each of which measures 45°. Hence:
Answer:
Value is x=8 and y=4
Step-by-step explanation:
Given : A right triangle 'A' hypotenuse length of x+4 and a leg of x,
and right triangle 'B' hypotenuse length of 3y and a leg length of y+4
To find : For what values of x and y are the triangles congruent by HL?
Solution :
Triangle A,
Hypotenuse: x+4
Leg: x
Triangle B,
Hypotenuse: 3y
Leg: y+4
Since the triangle A and B are congruent so, the sides of triangles are equal.
(Hypotenuse are equal) ..........[1]
and (Legs are equal) ..........[2]
Solving the equation of system,
Put the value of x from [2] in [1],
Substitute y in [2],
Therefore, The value of x=8 and y=4
Verifying for the values of x and y:
Triangle A,
Hypotenuse: x+4=8+4=12
Leg: x=8
Triangle B,
Hypotenuse: 3y=3(4)=12
Leg: y+4=4+4=8
Both hypotenuses and both legs are equal hence they are congruent.
Answer:
a(1)= -3
a(n)=a(n-1) (-3)
Step-by-step explanation:
hope this helps
Answer:
I cant help unless i have workable units (0.5) is not a point
but im guessing that you were trying to say (0,5) in which case its
7.07106781187
its a triangle
5 on one side
5 on the other
solve for the hypotenuse
hypotenuse =
hypotenuse = 7.07106781187
I hope this helps!
Answer:
50 feet
Step-by-step explanation:
Hope this helps!