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bob bundy
2012-10-09 07:36:24

Those are Euclidean lines ... so they are infinitesimally thin.

I'm going to pretend that your drawing shows the first triangle and the one that is congruent to it.

Bob

bobbym
2012-10-09 06:47:11

Hi;

I see the image. Put the lines that make up the sides on a diet.

zee-f
2012-10-09 06:45:32

3aaaa here is  what I came up with

bob bundy
2012-10-09 06:31:34

ok that should be fun

zee-f
2012-10-09 06:28:59

Ok I will show you what I drew in conclusion to what my mind came up with

Zee

bob bundy
2012-10-09 06:23:36

When you do pythagoras theorem you will learn the the right angled triangle with two sides of 1 has a longest side of root 2

But you don't have to know this to do the question.

I have a triangle with sides of 1 and a side of SQRT(2), with an angle of 45o and an angle of 90o.

You are told all three sides and all three angles.  Because the longest side must be opposite the largest angle the 90 must be between the two sides of 1.

If you do the following construction, only one triangle is possible (if you allow that all rotations and reflections are really the same)

(i)  Draw a side with length 1.

(ii) At one end make a 90 degree angle.

(iii) Make this second side also have length 1.

(iv)  You now have all three points for the vertices of the triangle so you can complete by drawing the third side.  It's length will be root 2 but you don't need to know this.  You have the congruency by SAS ( S = S = 1 and A = 90)

Bob

zee-f
2012-10-09 06:11:05

Thank you so much for all the help and time you are giving me ! )

But the thing I don't get is now I have an angle and a side that are congruent because (A) doesn't say it has a side of SQRT(2) and the question says the triangle has sides of 1 and a side of SQRT(2), with an angle of 45° and an angle of 90°. So in what  theorem are they congruent side angle side SAS ?

Zee

bob bundy
2012-10-09 06:00:07

Below one diagram for this problem.

The triangle is isosceles because it has two sides equal and the third is the longest.

Bob

zee-f
2012-10-09 05:58:48

ok

bob bundy
2012-10-09 05:52:38

Stay on-line.  I'll draw a diagram.

Bob

zee-f
2012-10-09 05:10:22

So (A) can be the answer because it has one as a side and 90 degree so side and side and angle.

bob bundy
2012-10-09 02:40:19

hi zee-f

The longest side of any triangle is always opposite the largest angle; and shortest is opposite smallest.

As root 2 is larger than 1, it must be opposite the 90 degrees, not adjacent to it.

Bob

zee-f
2012-10-09 02:35:16

I answered this question and I choose (B) and it was correct thanks for all the help!

But I am stuck on this question bellow(#14) well first I answered B and it was incorrect then I said:
My new answer would be (F) a triangle with an angle of 90o, then a side of SQRT(2), then an angle of 45o.

I have two corresponding angles that are congruent which are angles (45°,45°) and (90°,90°) and the corresponding sides (SQRT(2)),(SQRT(2)) between the angles are congruent.

So,according to the angle-side-angle theorem (ASA)the triangles are congruent.
And that was incorrect my teacher said #14 is incorrect.  The right angle would not be adjacent to the hypotenuse of the triangle. I am really confused help plzzzz

14. I have a triangle with sides of 1 and a side of SQRT(2), with an angle of 45o and an angle of 90o. Which of the following would be congruent to it? (You will need to use what you've learned about triangles and angle / side relations, as well as your knowledge of the rules of congruence to fill in the gaps and answer the question. Sketches may be helpful.)
A a triangle with a side of 1, then an angle of 90o, and a side of 1
B a triangle with a side of 1, then an angle of 90o, then a side of SQRT(2)
C a triangle with the angles 45o, 45o, 90o
D a triangle with sides of 1 and 1
E a triangle with a side of 1, then an angle of 45o, then a side of 1
F a triangle with an angle of 90o, then a side of SQRT(2), then an angle of 45o

bob bundy
2012-10-08 20:04:40

hi zee-f and bobbym

This topic is called 'proportion' and particularly 'similar triangles'.

When two shapes have the same angles or one is an exact enlargement of the other, they are said to be similar.

I've had a go at a diagram based on what you have written but I've hit two problems with trying to offer a solution.

Firstly, you need all the angles in the pair of triangles to be equal for the triangles to be similar.  I've taken that to be true in my diagram, but you only say CAB = FDE.  The base lines (BC and EF) could still be going in different directions.

Secondly, to work out the scale factor for the enlargement (once you know there is an enlargement) you need to know a measurement on one shape and the corresponding measurement on the other.  From your description we haven't got that.

You could do it if the '1' is the height of the smaller triangle.  Then the enlargement is 4.5/1 so the base BC = 1.43 x 4.5/1

Bob

bobbym
2012-10-08 14:24:04

Hi;

I sure wished I had a drawing to look at.