What else would need to be congruent to show that ABC XYZ by ASA?
2 answers:
Answer:
Step-by-step explanation:
In the given picture , there rae two triangles ΔABC and ΔXYZ.
It is given that ∠X≅∠A and ∠Y≅∠B
To prove both the triangles are congruent by ASA postulate, we need the corresponding included side of the given congruent pairs of angles.
The included side of ∠X and ∠Y is XY
The included side of ∠A and ∠B is AB
Thus, the additional information we neewd to prove the given triangle congruent by ASA is
- <em> ASA postulate tells that if two angles and the included side of one triangle are equal or congruent to two angles and the included side of another triangle, then the triangles are said to be congruent. </em>
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So there are 3 siblings: the first twin, the second twin, and their older sister.
Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11
Representing this next part may be a little hard to show, but i'll do my best :)
Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
Now you substitute in (s - 11) for t because s = t - 11.
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
Using the quadratic formula, you get:
Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.
Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.
Since the sister is older by 11 years, you can represent their relationship with the following equation;
age of twin = age of older sister - 11
t = s - 11
Representing this next part may be a little hard to show, but i'll do my best :)
Adding the ages together can be represented like this;
total age = t + t + s
If the product of their ages ( t * t * s ) is 1181 more than the sum, you can show it like this:
Now you substitute in (s - 11) for t because s = t - 11.
Factor:
Since it's a third-degree equation, I just entered it into a polynomial solver in my calculator. There was only one factor listed, x = 19. Using (s - 19) = 0 as a factor, the equation becomes the following:
Using the quadratic formula, you get:
Since you have a square root of a negative number, the answer will be imaginary. You cannot have an age that is imaginary, so the age of the older sister (s) is 19 years.
Because t = s - 11, that means that t = (19) - 11 = 8.
t is the age of the twins, so the twins are 8 years old.