Problem 1
The triangles share an overlapping angle at the very top. This is one pair of congruent angles. Another pair could be any of the corresponding angles formed by the parallel lines, and the transversals. We only need 2 pairs of congruent angles to use the AA (angle angle) similarity theorem.
Once we know the triangles are similar, we set up the proportion below and solve for x.
6/(x-1) = (6+x)/(2x+4)
6(2x+4) = (x-1)(6+x)
12x+24 = 6x+x^2-6-x
12x+24 = x^2+5x-6
0 = x^2+5x-6-12x-24
x^2-7x-30 = 0
(x-10)(x+3) = 0
x-10 = 0 or x+3 = 0
x = 10 or x = -3
Ignore negative x values because we cannot have negative lengths.
Therefore, x = 10 is the only plausible solution.
<h3>Answer: x = 10</h3>
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Problem 2
Notice how 12/9 = (4*3)/(3*3) = 4/3
While 28/21 = (4*7)/(3*7) = 4/3
We end up with 4/3 for both which allows us to say 12/9 = 28/21 is a true statement. From this, we know the triangles are similar due to the SAS similarity theorem. The last bit of info needed really is the set of congruent vertical angles in between the mentioned sides.
Let's set up a proportion to solve for x.
(4x-4)/18 = 12/9
9(4x-4) = 18*12
36x-36 = 216
36x = 216+36
36x = 252
x = 252/36
x = 7
<h3>Answer: x = 7</h3>
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Problem 3
Both triangles are equilateral. This is due to each triangle having the same tickmarks for all three sides. Every equilateral triangle has all three angles of 60 degrees. We then use the AA theorem to prove any two equilateral triangles are similar.
Let's solve for x.
(10x-10)/(2x) = 10/4
4(10x-10) = 2x*10
40x-40 = 20x
40x-20x = 40
20x = 40
x = 40/20
x = 2
<h3>Answer: x = 2</h3>
Answer:
Yes, the shapes are similar. Note, the angles are equivalent and the sides are scales of each other satisfying the requirements for similarly.
Step-by-step explanation:
For a shape to be similar there are two conditions that must be met. (1) Must have equivalent angles (2) Sides must be related by a scalar.
In the two triangles presented, the first condition is met since each triangle has three angles, 90-53-37.
To test if the sides are scalar, each side must be related to a corresponding side of the other triangle with the same scalar.
9/6 = 3/2
12/8 = 3/2
15/10 = 3/2
Alternatively:
6/9 = 2/3
8/12 = 2/3
10/15 = 2/3
Since the relationship of the sides is the scalar 3/2 (Alternatively 2/3), then we can say the triangles meet the second condition.
Given that both conditions are satisfied, then we can say these triangles are similar.
Note, this is a "special case" right triangle commonly referred to as a 3-4-5 right triangle.
Cheers.
Answer:
7 1/17 shifts
Step-by-step explanation:
That would be 7 1/2 divided by 1 1/16
= 15/2 / 17/16
= 15/2 * 16/17
= 15 * 8 / 17
= 120/17
= 7 1/17 shifts
Answer:
Slope intercept form: y= 
x-5
The answer is 50%.
Divide 2.25 by 1.50. That equals 1.5. That’s the equivalent to 50% because if you subtract 1 from 1.5 and multiply by 100. You get the same answer. Only do that for numbers greater than one, otherwise it won’t work
