#1
find the value of x if RS = 4(x-3)+6 and RT = 5(2x-6).
x= 12
x= 6
x= 4***
x= 3
#2
which of the following statements are always true? Choose all that apply.
If the circumcenter of a triangle lies on the triangle, then the triangle is a right triangle.
The incenter of a triangle is equidistant from all three vertices.
The incenter of a triangle always lies with in the triangle.***
The circumscribed in and circumscribed about isosceles triangle that have the same center.***
You can circumscribe a circle about any three points in a plane.
Can someone please check these?
Bisectors in triangles practice
1. C
2. B, D, F
3. A, C
4. B
5. D
6. A, C
7. D
8. D, C
The questions with multiple answers either have multiple parts or just multiple answers.
Your welcome is right!! 100%! Thanks so much!!
Still correct as of November 2021
you're welcome is still correct
This was really confusing for me.
For question 1, to find the value of x, we need to solve the equations RS = 4(x-3) + 6 and RT = 5(2x-6).
First, let's simplify RS = 4(x-3) + 6:
RS = 4x - 12 + 6
RS = 4x - 6
Next, let's simplify RT = 5(2x-6):
RT = 10x - 30
Now we have the following equations:
RS = 4x - 6
RT = 10x - 30
Since we want to find the value of x, we can set RS and RT equal to each other:
4x - 6 = 10x - 30
Now, let's solve for x. We'll bring the x terms to one side and the constants to the other side:
4x - 10x = -30 + 6
-6x = -24
To isolate x, we'll divide both sides by -6:
x = (-24)/(-6)
x = 4
Therefore, the value of x is 4.
For question 2, let's analyze each statement:
"If the circumcenter of a triangle lies on the triangle, then the triangle is a right triangle."
This statement is not always true. While it is true that in a right triangle, the circumcenter lies on the triangle, this does not hold true for all triangles.
"The incenter of a triangle is equidistant from all three vertices."
This statement is always true. The incenter of a triangle is the center of the inscribed circle, and by definition, it is equidistant from all three vertices.
"The incenter of a triangle always lies within the triangle."
This statement is always true. The incenter is always located within the triangle, and it is the intersection point of the angle bisectors of the triangle.
"The circumscribed in and circumscribed about isosceles triangles that have the same center."
This statement is true. For any isosceles triangle, the circumcenter and the incenter have the same location. It means that the circumcircle (circumscribed circle) and the incircle (inscribed circle) of an isosceles triangle share the same center.
"You can circumscribe a circle about any three points in a plane."
This statement is not always true. It is only true when the three points are not collinear (lie on the same line). If the three points are collinear, it is not possible to circumscribe a circle about them.
Based on the explanations provided, the correct answers for question 2 are:
- The incenter of a triangle always lies within the triangle.
- The circumscribed in and circumscribed about isosceles triangles that have the same center.
#1 No way to tell. What is the relationship between RS and RT?
If RS=RT, then x=4 is correct.
#2
choices A,C,E are true