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25 Oct 2021, 02:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
64% (01:18) correct
36%
(01:21)
wrong
based on 92
sessions
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Not Attempted Yet
In the above diagram, triangle ABC is isosceles with AB = AC. Which of the following statements provides a valid reason for concluding that x = y?
I. ∠B = 45°
II. K is the midpoint of BC
III. AK is the altitude to the base BC
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Attachment:
1.png [ 5.93 KiB | Viewed 2809 times ]
RanonBanerjee
Joined: 04 Dec 2020
Last visit: 11 Mar 2025
Posts: 35
Own Kudos:
Given Kudos: 153
Concentration: Technology, Strategy
Schools: Fuqua '27 (S)
01 Nov 2021, 11:21
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B & D both seems correct to me.
If we take statement II alone, K is the midpoint of BC. Therefore AK is the median. Now for an isosceles triangle, median drawn to the base is the altitude and the angle bisector. That gives X=Y.
Now separately, if we take option III, AK is the altitude to the base. In case of isosceles triangle, the altitude drawn to the base, is the median and angle bisector. So this statement alone will give X=Y.
Had I not seen the spoiler, I would have answered B.
Can someone please clarify?
Posted from my mobile device
If we take statement II alone, K is the midpoint of BC. Therefore AK is the median. Now for an isosceles triangle, median drawn to the base is the altitude and the angle bisector. That gives X=Y.
Now separately, if we take option III, AK is the altitude to the base. In case of isosceles triangle, the altitude drawn to the base, is the median and angle bisector. So this statement alone will give X=Y.
Had I not seen the spoiler, I would have answered B.
Can someone please clarify?
Posted from my mobile device
01 Nov 2021, 17:45
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If we take second statement alone , we can prove the two angles are equal by congruence (SSS) . I thought its B but the answer says its D . I don't understand why we will need both statement II and III to prove that . Can someone please explain?
