Problem 2
Answer: Choice A) triangle AED is similar to triangle ACB
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Step-by-step explanation:
A) This is true since dilations result in similar figures
B) The triangles are not congruent. They have different sizes. Dilations with scale factors other than 1 results in non-congruent triangles.
C) AED has an area of 2*3/2 = 3 while ACB has an area of 4*6/2 = 12. So saying "the area of triangle AEB is half the area of ACB" is false. Changing "half" to "quarter" would fix the issue.
D) The scale factor is 2, so the perimeter of the larger triangle is twice that of the smaller. So the statement made in choice D is false.
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Problem 3
Answer: Choice C) 40 degrees
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Step-by-step explanation:
Angle ACD is the bottom left angle of the parallelogram.
Angle ABD is the top right angle of the parallelogram.
These two angles are opposite angles. They are congruent angles.
Angle ACD = Angle ABD
4x+4 = 6x-14
6x-4x = 4+14
2x = 18
x = 9
Use x = 9 to find that...
Angle ACD = 4*x+4
Angle ACD = 4*9+4
Angle ACD = 36+4
Angle ACD = 40 degrees
Side Note: Angle ABD is also 40 degrees since 6x-14 = 6*9-14 = 54-14 = 40
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Problem 4
Answer: Choice C) VS < VU
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Step-by-step explanation:
Hinge Theorem: The larger the angle, the longer the opposite side.
Angle VTU is larger than angle VTS
So VU is larger than VS
Or VS is smaller than VU
VS < VU
Note: We don't have enough info to compare any other pair of segments (such as ST and TU)