Why is A not sufficient??
From A we know that ACD is isoceles right triangle with hypothenuse AD.
Angle CAD is 45° and angle ACD is 90° so CDA must be 45°.
CD should be 5/Sqroot2.
And BD should be 2*5/Sqroot2
Why am i wrong?
Although the statement A doesn't say isoceles, you can deduce it thanks to the statement itself.
The perpendicular cuts the right triangle into two triangles creating a right angle (ACD) and splitting the right triangle ABD in two (45°). So you can deduce that angle ADC is 45°.
So A should be sufficient. Am I clear?
Thx
MGMAT Geometry Triangle
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- codesnooker
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There is no such theorem. You are trying to predict the angle according to the given figure. See I can read your mind.nadontheway wrote:Why is A not sufficient??
From A we know that ACD is isoceles right triangle with hypothenuse AD.
Angle CAD is 45° and angle ACD is 90° so CDA must be 45°.
CD should be 5/Sqroot2.
And BD should be 2*5/Sqroot2
Why am i wrong?
Although the statement A doesn't say isoceles, you can deduce it thanks to the statement itself.
The perpendicular cuts the right triangle into two triangles creating a right angle (ACD) and splitting the right triangle ABD in two (45°). So you can deduce that angle ADC is 45°.
So A should be sufficient. Am I clear?
Thx
The figure is totally wrong. Get a rule and a D, try to make a figure having angles B (30 degree), D (60 degree) and A (90 degree).
Then try to draw the perpendicular from A t on BD. You will get your answer.
PS: You are trying to apply bisect theorem which is not fit over here.
Let me know if you still have any confusion.
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Thanks a lot codesnooker. I really appreciate.
My confusion is based on the definition of Perpendicular lines itself: "Perpendicular lines form right angles". Based on that information, I concluded that angle C must be 90°.
What do you think?
My confusion is based on the definition of Perpendicular lines itself: "Perpendicular lines form right angles". Based on that information, I concluded that angle C must be 90°.
What do you think?
- codesnooker
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Did you try to sketch the figure that I mentioned in my earlier post on this topic.nadontheway wrote:Thanks a lot codesnooker. I really appreciate.
My confusion is based on the definition of Perpendicular lines itself: "Perpendicular lines form right angles". Based on that information, I concluded that angle C must be 90°.
What do you think?
The angle C will be equal to 90 degree only when A and D are equal to 45 degree. However that is not necessary at all. The relation between A and D is
A + D = 90 degree
So A and D could be anything, however their sum should be always equal to 90 degree.
Sketch the figure and you can derive it yourself.
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I sketch the figure you mentioned in your earlier post only conceptually (I don't have a D;)).
I see that A+D= 90°.
With the perpendicular AC, A can be 45° or 30° and D can be 45° or 60° or anything else as long as A+D=90°. So at this stage we don't know if ACD is isoceles triangles or equilateral triangle or someting else. I can see that now. So A is not sufficient to determine BD.
But because perpendicular lines form right angles C must be 90° whatever angle A and D measure. Is that correct?
I see that A+D= 90°.
With the perpendicular AC, A can be 45° or 30° and D can be 45° or 60° or anything else as long as A+D=90°. So at this stage we don't know if ACD is isoceles triangles or equilateral triangle or someting else. I can see that now. So A is not sufficient to determine BD.
But because perpendicular lines form right angles C must be 90° whatever angle A and D measure. Is that correct?
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Of course, that's what PERPENDICULAR termed for.nadontheway wrote: But because perpendicular lines form right angles C must be 90° whatever angle A and D measure. Is that correct?
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I can't believe how easy this problem is. I really need to focus and handle geometry concepts...
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The correct answer is C
Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD).
We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD.
If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5sqrt2.
Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD).
We also know that angle BAD is a right angle, so side BD is the hypotenuse of right isosceles triangle BAD.
If each leg of the triangle is 5, the hypotenuse (using the Pythagorean theorem) must be 5sqrt2.