A.) The SAS Triangle Congruence Postulate states that if if a pair of corresponding sides, a pair of corresponding angles, and another pair of corresponding sides in two triangles are congruent, then the two triangles are congruent. Therefore, we can see that in both triangles, we are only shown a corresponding, congruent right angle. We need two pairs of sides with the corresponding right angles to prove that the triangles are congruent via SAS. We would need to know the length of side VX, and it’s corresponding side length, XV. We would also need to know the side lengths of WV and it’s corresponding side length, XK. We would then need some sort of symbol to represent a congruent relationship if the side lengths are congruent. Then, we would have two pairs of corresponding, congruent sides, and a pair of corresponding, congruent angles. Then, we would have a Side-Angle-Side.
b.) We are given two triangles with a pair of corresponding, congruent sides. We need to have a pair of corresponding, congruent angles, another pair of corresponding, congruent sides to follow SAS. Therefore, we would need to know the angle measures of angles UVW and KVM. We know that they are vertical angles, so they are indeed congruent. Now, we would need to know the side lengths of sides WV and VM. If those sides are congruent, then we have a pair of corresponding, congruent sides, a pair of corresponding, congruent angles, and another pair of corresponding, congruent sides, making SAS.
c.) The Angle Side Angle Postulate states that if there is a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, and another pair of corresponding, congruent angles in two triangles, then the two triangles are congruent. We have a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, but we need another pair of congruent, corresponding angles. Therefore, we would need to know the angle measures of angles MLK and STU. Then we would have a a pair of corresponding, congruent angles, a pair of corresponding, congruent sides, and another pair of corresponding, congruent angles.
At the end of the game you owned 13 cents if 71% of your rolls are successful and 29% of your rolls are unsuccessful option first is correct.
<h3>What is probability?</h3>
It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Every time you roll a 1 or 2 you are successful, and your friend will pay you $1. Every time you roll a 3, 4, 5 or 6, you must pay your friend $2.
71% of your rolls are successful:
= 1×0.71
= $0.71 (won)
29% of your rolls are unsuccessful
= 2×2.9
= $0.58 (lose)
The amount owned = 0.71 - 0.58 = $0.13 = 13 cents
Thus, at the end of the game you owned 13 cents if 71% of your rolls are successful and 29% of your rolls are unsuccessful option first is correct.
