Triangle XYZ has been dilated to form triangle LMN. What is the least amount of information needed to prove the two triangles ar
e similar?
a. Two pairs of corresponding angles and one pair of corresponding sides
b. Two pairs of corresponding sides and one pair of corresponding angles
c. Two pairs of corresponding angles
d. Two pairs of corresponding sides
a. Two pairs of corresponding angles and one pair of corresponding sides
b. Two pairs of corresponding sides and one pair of corresponding angles
c. Two pairs of corresponding angles
d. Two pairs of corresponding sides
1 answer:
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Answer: x = 6
Step-by-step explanation:
Because we are given that the two figures are already similar, we can set up a proportional relationship to determine the value of x. Since the larger rectangle has a width of 21 and the smaller rectangle has a width of 7, those values can be used as the numerators in the proportion. Since the larger rectangle's length is x plus the additional 3 units on the smaller rectangle, x+3 and 3 can be used as the denominators in the proportion.
Next, we set up the proportion as follows:
Then, you cross multiply to get the equation:
After solving down algebraically, you get the value of x to be 6.
I hope this helps!