SAS for similar triangles is NOT the same theorem as we used for congruent triangles. To show triangles are similar, it is sufficient to show that two sets of corresponding sides are in proportion and the angles they include are congruent.
Theorem:
If an angle of one triangle is congruent to the corresponding angle of another triangle and the lengths of the sides including these angles are in proportion, the triangles are similar.
Answer: 31 : 9
Step-by-step explanation:
Assume the following:
Alice's amount = P
Bob's amount = Q
Amount received = n
If Alice receives $n$ dollars from Bob ;then she will have $4$ times as much money as Bob.
P + n = 4(Q - n)
P + n = 4Q - 4n
P = 4Q - 4n - n
P = 4Q - 5n - - - - (1)
If, on the other hand, she gives $n$ dollars to Bob, then she will have $3$ times as much money as Bob
P - n = 3(Q + n)
P - n = 3Q + 3n
P = 3Q + 3n + n
P = 3Q + 4n - - - - - - (2)
Equating both equations - (1) and (2)
4Q - 5n = 3Q + 4n
4Q - 3Q = 4n + 5n
Q = 9n
Express P in terms of n, use either equation (1) or (2)
From equation 2:
P = 3Q + 4n
Substituting Q = 9n
P = 3(9n) + 4n
P = 27n + 4n
P = 31n
Alice's amount = P, Bob's = Q
Ratio = P:Q
31 : 9
Answer:
The meaning of each statement is shown below.
Step-by-step explanation:
Assume that the given statements are
(a) c(0)=0
(b) c(3)=c(8)
(c) c(n)=29
(d) c(13)<c(12)
Let c(t) be the number of customers in a restaurant t hours after 8 A.M.
We need to find the meaning of each given statement.
(a) c(0)=0 means the number of customers 0 hours after 8 A.M (i.e., 8 A.M.) is 0.
(b) c(3)=c(8) means the number of customers 3 hours after 8 A.M (i.e., 11 A.M.) is equal to the number of customers 8 hours after 8 A.M (i.e., 4 P.M.).
(c) c(n)=29 means the number of customers n hours after 8 A.M is 29.
(d) c(13)<c(12) means the number of customers 13 hours after 8 A.M (i.e., 9 P.M.) is less than the number of customers 12 hours after 8 A.M (i.e., 8 P.M.).
The answer to the question is B.
Answer:
Three-fourths
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
∠QSR≅∠XZY ---> given problem
∠QRS≅∠XYZ ---> given problem
so
△QRS ~ △XYZ ----> by AA Similarity theorem
Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
That means
∠Q≅∠X
∠R≅∠Y
∠S≅∠Z
<em>In the right triangle XYZ</em>
Find the tangent of angle X
---> opposite side angle X divided by adjacent side angle X
substitute the given values
Simplify
Remember that
∠Q≅∠X
so
therefore
---->Three-fourths
