Question

In the diagram: AB DEandAC - DF . Additionally, mZA = 4x + 10andmZD= -3x + 80 What value of x would prove the triangles are congruent by SAS? 10 0 40 90

Answer 1

x = 10

Step-by-step explanation:

SAS means Side-Angle-Side. So, two triangles are congruent if they have 2 sides that are congruent and the angle in the middle is also congruent.

In this case, we have 2 sides congruent: AB with DE and AC with DF.

So, the triangles are congruent if the angles A and D are also congruent.

Therefore, we can write the following equation:

`\begin{gathered} m\angle A=m\angle D \\ 4x+10=-3x+80 \end{gathered}`

So, solving for x, we get:

`\begin{gathered} 4x+10-10=-3x+80-10 \\ 4x=-3x+70 \\ 4x+3x=-3x+70+3x \\ 7x=70 \\ (7x)/(7)=(70)/(7) \\ x=10 \end{gathered}`

Therefore, the value of x that prove that the triangles are congruent is x = 10