What type of triangle is shown below check all that apply
2 answers:
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Part 1.
A. x=0 can be used for function that have x≤1, so f(x) =x²
B.You need substitute x by 0. x=0,
then
f(0) = 1) x² =0² =0 x≤1
Part 2.
A. f(x) =x², Graph is attached.
B. f(x) =2x+1, Graph is attached.
C. The functions will change in the point x=1
For f(x) =x² , x ≤1 ; f(1) = 1. The point (1,1) is included, the dot should be filled (closed).
For the function f(x)=2x+1, x>1. The point f(1)=3 is not included, the dot should be empty(open).
D. Point(1,1) is closed(filled circle), point (1,3) is open(empty circle).
A. x=0 can be used for function that have x≤1, so f(x) =x²
B.You need substitute x by 0. x=0,
then
f(0) = 1) x² =0² =0 x≤1
Part 2.
A. f(x) =x², Graph is attached.
B. f(x) =2x+1, Graph is attached.
C. The functions will change in the point x=1
For f(x) =x² , x ≤1 ; f(1) = 1. The point (1,1) is included, the dot should be filled (closed).
For the function f(x)=2x+1, x>1. The point f(1)=3 is not included, the dot should be empty(open).
D. Point(1,1) is closed(filled circle), point (1,3) is open(empty circle).
Answer:
We consider a triangle ABC as attached in the answer.
We draw a line parallel to AB that passes through point C.
Angles C and C' are vertical angles, therefore ∠C = ∠C'.
Angles B and B' are corresponding angles, therefore ∠B = ∠B'.
Angles A and A' are corresponding angles, therefore ∠A = ∠A'.
it can be seen that angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.
The three angles A', B', and C' form together a straight angle so, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.
This proofs that sum of angles of a triangle is equal to 180.
