Let us denote the semi arcs as congruent angles. This means that angles FEJ and EFJ are congruent (That is, they have the same measure). Since angles FEJ and EFJ have the same measure, this implies that sides EJ and FJ are equal. Since angles EJK and FJH are supplementary angles to angle EJF, this implies that EJK and FJH have the same measure.

Using the Angle Side Angle (SAS) criteria, we determine that triangles EKJ and triangle FJH are congruent. This implies that sides EK and FH are equal and that angles EKJ and FHJ are congruent. Note that angle EKJ is the same as EKF and that FHJ is the same as FHE.

Once again, since angles EKF and FHJ are congruent, and angle EKD is supplementary to the angle EKJ when angle FHG is supplementary to angle FHJ, then we have that angles EKD and angle FHG are congruent.

Using again the SAS criteria, we determine that triangles EKD and FHG are congruent.

From this reasoning, we have proved the following facts:

Triangle DEK is congruent to triangl GFH

Angle EKF is congruent to angle FHE

Segment EK is the same as segment FH

4 0

10 months ago

How much simple interest rate would earn if had $10,000 and you were being paid 5% for 15 months?

lakkis [162]

Here is the interest equation: I=prt
Where I is interest, p is principal, r is rate and t is time(in years).
Substitute with known values.

I= prt
I= 10000(.05)(1 and 1 over 4)
I= 625
Answer: $625 for 15 months.

4 0

3 years ago

On the number line below, P represents a number. What is the value of the opposite of that number? A number line from negative 4

Temka [501]

Answer:

$-1\frac{1}{4}$