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Updated on: 07 Aug 2018, 05:00
Originally posted by EgmatQuantExpert on 22 Nov 2016, 05:32.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:00, edited 3 times in total.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:00, edited 3 times in total.
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Exercise Question #2 Common Mistakes in Geometry Questions
In the triangle above, what is the measure of Angle CDB?
(1) Angle CAB = Angle ACB = 30°
(2) AB = BC = BD
Answer Choices
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Detailed solution will be posted soon.
In the triangle above, what is the measure of Angle CDB?
(1) Angle CAB = Angle ACB = 30°
(2) AB = BC = BD
Answer Choices
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Detailed solution will be posted soon.
20 Aug 2017, 11:27
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Statement 2 is not sufficient here. The solutions above that contend it is sufficient are all making assumptions that you don't know to be true. For example, you don't know that the vertical-looking line bisects the 90 degree angle - you'd need to know that the large triangle was isosceles (AC = CD) to conclude that, and we don't know whether AC = CD is true. Nor do we know that the vertical-looking line is perpendicular to the horizontal-looking line (i.e. we don't know that AD is perpendicular to BC). If you did know either of those things, Statement 2 would be sufficient, but we don't know those things.
You can see visually why Statement 2 is not sufficient. Draw a circle, with center B, and draw a diameter AD. Then let C be any other point on the circumference of the circle. Draw the triangle ADC. We must get a 90 degree angle at C, since we're connecting a diameter to a point on the circle, and every radius is the same length, so BC = BA = BD. By moving the point C around the circumference, you can easily change the size of the two smaller angles in triangle ADC (the angles at A and at D). Now just erase the circle and you have the same situation as is described in this question, when using Statement 2 alone. Since we just saw we can move point C around and change the size of angle CDB, the information can't be sufficient.
You can see visually why Statement 2 is not sufficient. Draw a circle, with center B, and draw a diameter AD. Then let C be any other point on the circumference of the circle. Draw the triangle ADC. We must get a 90 degree angle at C, since we're connecting a diameter to a point on the circle, and every radius is the same length, so BC = BA = BD. By moving the point C around the circumference, you can easily change the size of the two smaller angles in triangle ADC (the angles at A and at D). Now just erase the circle and you have the same situation as is described in this question, when using Statement 2 alone. Since we just saw we can move point C around and change the size of angle CDB, the information can't be sufficient.
14 Sep 2017, 21:51
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getitdoneright
Yes, angle ACD is 90 degrees and ACB + BCD = 90 degrees but the point is that we don't know whether CB is perpendicular to AD. Not knowing that, how are you getting that (2) is sufficient?
