Question

explain 2 applying
read explain 2 and complete your turn #1 - 2 (adapted from lesson 5.4). show all your work
you can use the sss triangle congruence theorem and other triangle congruence theorems to solve real wor
problems that involve congruent triangles.
example find the value for x that results in △abc ≅ △jkl.
if △abc ≅ △jkl, then (overline{bc}congoverline{kl}).
(bc = kl) definition of congruence
(4x - 6 = 3x - 4) substitution
(x - 6 = - 4) subtraction property of equality
(x = 2) addition property of equality
your turn

1. find the values for x that results in △fgh ≅ △tuv.
2. find the values for y that results in △fgh ≅ △tuv.

Explanation:

Step1: Determine the congruent sides for \(x\)

Since \(\triangle FGH\cong\triangle TUV\), the corresponding sides \(GH\) and \(UV\) are equal.
\(8x - 12 = 12\)

Step2: Solve the equation for \(x\)

Add \(12\) to both sides:
\(8x-12 + 12=12 + 12\)
\(8x=24\)
Divide both sides by \(8\):
\(x=\frac{24}{8}=3\)

Step3: Determine the congruent angles for \(y\)

In \(\triangle TUV\), using the angle - sum property of a triangle (\(180^{\circ}\)), the angle at \(T\) is \(180-(90 + 30)=60^{\circ}\).
Since \(\triangle FGH\cong\triangle TUV\), the angle at \(T\) (\((7y + 4)^{\circ}\)) is equal to the angle at \(F\) (\(60^{\circ}\))
\(7y+4 = 60\)

Step4: Solve the equation for \(y\)

Subtract \(4\) from both sides:
\(7y+4-4=60 - 4\)
\(7y=56\)
Divide both sides by \(7\):
\(y=\frac{56}{7}=8\)

Answer:

1. \(x = 3\)
2. \(y = 8\)