The values of x and y for which the triangles are congruent by HL are x = v + 10 and y = 1/4v + 11/4.
Let’s find the values of x and y for which the triangles are congruent by HL.
We are given two equations:
x+1=4y
v+11=4y
We can solve this system of equations using elimination.
Steps to solve:
1. Rearrange terms in standard form:
x−4y=−1
−4y+v=−11
2. Eliminate y:
x−v=10
y− 1 /4 v= 11 /4
3. Solve for x and y:
x=v+10
y= 1 / 4 v+ 11/4
Therefore , the values of x and y for which the triangles are congruent by HL are x = v + 10 and y = 1/4v + 11/4.