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Triangle ABC is an isosceles triangle.
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25 Oct 2021, 05:14
25 Oct 2021, 05:14
Expert Reply
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Question Stats:
38% (01:07) correct
61% (00:56) wrong based on 18 sessions
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Triangle ABC is an isosceles triangle.
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The probability that the altitude drawn from A to \(\overline{BC}\) is congruent to the median drawn from A to \(\overline{BC}\) |
\(\frac{1}{3}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Triangle ABC is an isosceles triangle.
[#permalink]
25 Oct 2021, 15:14
25 Oct 2021, 15:14
2
If the isosceles triangle ABC is also equilateral, then regardless of which point you choose as A and side BC, the altitude is congruent to the median (i.e. probability is 1). If ABC is not equilateral, then this is true only for one vertex (i.e. probability is 1/3). Therefore, the answer is D.
Re: Triangle ABC is an isosceles triangle.
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07 Nov 2021, 06:16
07 Nov 2021, 06:16
The possibilities can also be given as:
1. AB=BC<=>AC
2. BC=AC<=>AB
3. AC=AB<=>BC
4. AB=BC=AC
Thus required probability for Scenario A is in case: 3. AC=AB<=>BC and 4. AB=BC=AC.
Hence, A=1/2
Thus A. Quantity A is greater.
1. AB=BC<=>AC
2. BC=AC<=>AB
3. AC=AB<=>BC
4. AB=BC=AC
Thus required probability for Scenario A is in case: 3. AC=AB<=>BC and 4. AB=BC=AC.
Hence, A=1/2
Thus A. Quantity A is greater.
