Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.
More Regents problems.
Geometry Regents, June 2013
Part I: Each correct answer will receive 2 credits.
1. If triangle MNP ≅ triangle VWX and PM is the shortest side of triangle MNP, what is the shortest side of VWX?
1) XV
2) WX
3) VW
4) NP
Answer: 1) XV
If two triangles are congruent, then the corresponding sides are congruent. When listing two congruent triangles, the order of the letters matters. In this example, angle M corresponds to angle V, etc.
2. In circle O shown in the diagram below, chords AB and CD are parallel.
If m AB = 104 and m CD = 168, what is m BD ?
1) 38
2) 44
3) 88
4) 96
Answer: 2) 44
Arcs AC and BD are equal in size because the chords are parallel. The FOUR chords together add up to 360 degrees. Don't forget the fourth chord.
272 + 2x = 360
2x = 88
x = 44
3. As shown in the diagram below, CD is a median of ABC.
Which statement is always true?
1) AD ≅ DB
2) AC ≅ AD
3) ∠ACD ≅ ∠CDB
4) ∠BCD ≅ ∠ACD
Answer: 1) AD ≅ DB
The definition of median is that D will be the midpoint of AB, so AD ≅ DB
Choice (2) could be true but usually will not be.
Choice (3) can never be true because ∠CDB is an exterior angle and is the sum of ∠ACD and ∠DAC.
Choice (4) would be true if CD were also an angle bisector, but it is only a median.
4. In the diagram below, under which transformation is ABC
the image of ABC?
1) D2
2) rx-axis
3) ry-axis
4) (x, y) --> (x-2, y)
Answer: 3) ry-axis
The preimage was flipped over the y-axis to get the image. So it is a reflection.
Choice (1) is a Dilation of scale 2 would have doubled the size. This didn't happen.
Choice (2) is a reflection over the x-axis, which would have flipped the image upside down.
Choice (4) would move the preimage two units to the left.
5. Line segment AB is a diameter of circle O whose center has coordinates (6,8). What are the coordinates of point B if the coordinates of point A are (4,2)?
1) (1,3)
2) (5,5)
3) (8,14)
4) (10,10)
Answer: 3) (8,14)
If the center is point O, (6, 8), then the distance from the point O to B is the same as the distance from point O to A. More to the point, point O is the midpoint of AB.
To get from A to O, you go 6 - 4 = 2 units to the right and 8 - 2 = 6 units up.
Moving (+2, +6) from O means that B is (6+2, 8+6) = (8, 14).
More to come. Comments and questions welcome.
More Regents problems.
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