Johnny is going to use ASA to prove that VWX=YZX.Which of these is a necessary step in Johnny's proof? A. Prove that WX= XZby CP
CTC.B. Prove that VW=YZ by CPCTC.C. Prove that VWX=YZX by alternate interior angles.D. Prove that VXW = YXZ by vertical angles.
1 answer:
In order to prove that two triangles are congruent using the ASA theorem, it is necessary to show two pairs of congruent angles and one pair of congruent sides of the triangles.
In the given diagram, there is already a pair of congruent triangles and a pair of congruent sides shown.
Then, in order to use the ASA theorem, we need to prove that there is another pair of congruent angles, one from each triangle.
Since the side VX must be adjacent to both angles involved in the procedure, then we need to show that the angle VXW is congruent to the angle YXZ, which is adjacent to the side YX.
This can be proven using the fact that VXW and YXZ are vertical angles.
Therefore, the necessary step in Johnny's proof is shown in option D)
You might be interested in
Answer:
a) 0.25
b) 0.25
c) 0.0625
Step-by-step explanation:
The complete question is:
Do you remember when breakfast cereal companies placed prizes in boxes of cereal? Possibly you recall that when a certain prize or toy was particularly special to children, it increased their interest in trying to get that toy. How many boxes of cereal would a customer have to buy to get that toy? Companies used this strategy to sell their cereal.
One of these companies put one of the following toys in its cereal boxes: a block (B), a toy watch (W), a toy ring (R), and a toy airplane (A). A machine that placed the toy in the box was programmed to select a toy by drawing a random number of 1 to 4. If a 1 was selected, the block (or B) was placed in the box; if a 2 was selected, a watch (or W) was placed in the box; if a 3 was selected, a ring (or R) was placed in the box; and if a 4 was selected, an airplane (or A) was placed in the box. When this promotion was launched, young children were especially interested in getting the toy airplane.
What is the probability of getting an airplane in the first cereal box?
Since the machine randomly selects toys, each toy has the same probability of being obtained in a cereal box.
Then, the total outcomes are 4 and the probability of getting an airplane in the first cereal box is 0.25 (25%).
What is the probability of getting an airplane in the second cereal box?
Two independent events do not change the probability of occurrence of one event or another.
The probability of getting an airplane in the second cereal box is 0.25 (25%).
What is the probability of getting airplanes in both cereal boxes?
P(1°∩2°)= P(1°) × P(2°) =
P(1°∩2°)= 0.0625 = 6.25%
Answer:
Option a. $2,040
Step-by-step explanation:
step 1
To find out the amount of the additional passive income last year, subtract the amount earned at her salaried job from Loretta’s income last year
so
step 2
Divide the additional passive income last year by 12 (number of months in a year)
therefore
approximately $2,400 per month