To find the value of b in congruent triangles ABC and DEF, where BC = 9b + 6 and EF = 3b + 36, we set up the equation 9b + 6 = 3b + 36 based on the property of congruent triangles. Rearranging and solving this equation, we get b = 5.
Step-by-step explanation:
The student is working on a geometry problem involving congruent triangles and algebraic expressions. Given that triangle ABC is congruent to triangle DEF (△ABC ≅ △DEF), we have the information that BC = 9b + 6 and EF = 3b + 36. By the property of congruent triangles, we know corresponding sides are equal, hence BC = EF.
Setting up an equation based on this property, we get:
Write down the equality based on the corresponding sides of congruent triangles: 9b + 6 = 3b + 36.
Rearrange the equation to solve for b: 9b - 3b = 36 - 6.
Simplify the equation: 6b = 30.
Divide both sides by 6 to isolate b: b = 30 / 6.
Therefore, the value of b is 5.
The definition or property used here is the Congruence of Triangles, which states that in two congruent triangles, all corresponding sides and angles are equal.