Question

1. if ( \triangle abccong\triangle def ), ( ab = 8 ), ( bc = 19 ), ( ac = 14 ), ( ef = 4x - 1 ), and ( de = y - 6 ), find the values of ( x ) and ( y ).

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), corresponding sides are equal. So \(BC = EF\) and \(AB=DE\).

Step2: Solve for \(x\)

Given \(BC = 19\) and \(EF = 4x - 1\), set up the equation \(4x-1=19\).
Add \(1\) to both sides: \(4x=19 + 1\), so \(4x=20\).
Divide both sides by \(4\): \(x=\frac{20}{4}=5\).

Step3: Solve for \(y\)

Given \(AB = 8\) and \(DE=y - 6\), set up the equation \(y-6=8\).
Add \(6\) to both sides: \(y=8 + 6=14\).

Answer:

\(x = 5\) and \(y = 14\)