Given triangle KLM is CONGRUENT to triangle NOP, KL = 2y, LM= 6, KM = 8, NP = 2x-2y, and ON = X. Determine the measures of x and y.
I drew out the two triangles and I know I’m gonna have to solve to get x and y but the two variables are confusing me so I’m not sure what I have to set them equal to.
If anyone could explain where to go or how they solved it would be greatly appreciated.
Matching up the corresponding sides, you have
2y = x
2x-2y = 8
so, substituting, you get
2(2y)-2y = 8
solve for y, then you can get x.
Alright so would x=8 and y=4
To solve for x and y, we can use the congruence of the triangles and the given side lengths.
Since triangle KLM is congruent to triangle NOP, their corresponding sides are equal in length.
Given:
KL = 2y
LM = 6
KM = 8
NP = 2x - 2y
Using the corresponding sides, we can set up equations:
KL = NP
2y = 2x - 2y
This equation represents the congruence of the corresponding sides KL and NP.
LM = ON
6 = x
This equation represents the congruence of the corresponding side LM and ON.
Now, we can solve the equations to find the values of x and y.
From the equation 2y = 2x - 2y, we can simplify it by combining like terms:
4y = 2x
2y = x
Substitute this value of x in the equation 6 = x:
6 = 2y
Divide both sides by 2 to solve for y:
3 = y
So, the value of y is 3.
Substitute this value of y in the equation 2y = x:
2(3) = x
Simplify:
6 = x
Therefore, the value of x is 6.
To summarize:
y = 3
x = 6
To determine the measures of x and y, we need to use the fact that triangle KLM is congruent to triangle NOP. Congruent triangles have corresponding sides and angles that are equal in measure.
Given that KL = 2y, LM = 6, KM = 8, NP = 2x - 2y, and ON = x, we can start by comparing the corresponding sides of the two triangles:
1. KL = NP:
Since KL = 2y and NP = 2x - 2y, we can set them equal to each other:
2y = 2x - 2y
2. LM = NO:
Since LM = 6 and NO = x, we can set them equal to each other:
6 = x
Now, let's solve these equations to determine the values of x and y:
1. KL = NP:
2y = 2x - 2y
Adding 2y to both sides: 4y = 2x
Dividing both sides by 2: 2y = x
2. LM = NO:
6 = x
Therefore, the measures of x and y are x = 6 and y = 3.
To summarize:
x = 6
y = 3