Question 283896: I have a triangle with sides of 1 and a side of SQRT(2), with an angle of 45° and an angle of 90°. Which of the following would be congruent to it?
a-a triangle with a side of 1, then an angle of 90°, and a side of 1
b-a triangle with a side of 1, then an angle of 90°, then a side of SQRT(2)
c-a triangle with the angles 45°, 45°, 90°
d-a triangle with sides of 1 and 1
e-a triangle with a side of 1, then an angle of 45°, then a side of 1
f-a triangle with an angle of 90°, then a side of SQRT(2), then an angle of 45°
I would be grateful for any assistance.
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! a triangle with angle 90 and 45 also has the other angle 45.
Any triangle with the same three angles is similar.
Any figure that is congruent is also similar but not all similar are congruent.A triangle with two 45 degrees angles is isosceles have two sides and two angles equal.
But in the original triangle we don't know which sides are equal, do we?
we also know that it is a right triangle and the hypotenuse is the largest side.
sqrt(2) > 1
so we can't have two sides with length sqrt(2)
a-a triangle with a side of 1, then an angle of 90°, and a side of 1
b-a triangle with a side of 1, then an angle of 90°, then a side of SQRT(2)
c-a triangle with the angles 45°, 45°, 90°
d-a triangle with sides of 1 and 1
e-a triangle with a side of 1, then an angle of 45°, then a side of 1
f-a triangle with an angle of 90°, then a side of SQRT(2), then an angle of 45°
Analysis
a- if a triangle has a 90 degree angle then the others add up to 90.
but if two are equal to 1 then it is also isosceles. and has 2 angles 45
a yes
b-the third side can be larger than 1 and the angles can be something else
c-they are similar but not necessarily congruent
d-it is isosceles and there for has two equal angles along with the equal sides.
the two sides are 1 does the third side have to be sqrt(2)?
e-if the two sides are equal and one angle is 45 does there have to be another angle of 45? can to ther angles be 135/2 sides equal to 1?
f-this triangle has two 45 degree angles and a side of sqrt(2) Doe the equal sides have to be 1 or can they both be sqrt(2)?
I did the first three (abc) and left you thinking on the last three (def)
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