Answer:
Here is the complete question.
Marie drew the triangle shown. She wants to draw a second triangle that is different from this one.
It is ____for Marie to draw a second triangle with different angle measures and the same side lengths.
It is____for Marie to draw a second triangle with different side lengths and the same angle measures.
Choices are Impossible and Possible.
"It is impossible for Marie to draw a second triangle with different angle measures and the same side lengths.
It is possible for Marie to draw a second triangle with different side lengths and the same angle measures."
Step-by-step explanation:
⇒As the triangle attached is having equal side lengths so its an equilateral triangle which is having [tex]60[/tex] degrees for all all of its angles.
And according to angle sum property of a triangle we know that,summation of all angle measures [tex]180\ (deg)[/tex].
Here in this equilateral triangle we can't change the measure of any of its sides as equally because,lets assign [tex]x[/tex] to any of its angles then [tex]x+x+x=180,3x=180,x=\frac{180}{3}=60[/tex] algebraically it is impossible so as geometrically.
⇒Second one is just the vice versa of the above where the angles can't be changed but the side lengths can be.
So,
It is impossible for Marie to draw a second triangle with different angle measures and the same side lengths.
It is possible Marie to draw a second triangle with different side lengths and the same angle measures.
