Question

Find the value of the variable that results in congruent triangles. Complete the explanation.
F
30°
30°
9 in.
9 in.
(2x) in.
(x + 4) in.
А
B
D
E
AC is congruent to DF, because AC
DF = 9 in. 2C is congruent
to ZF. EF
must correspond to BC. The triangles (select) » congruent by the (select) Triangle
Congruence Theorem only when x = |

Answer 1

Answer:

$\overline{AC}$ is congruent to $\overline{DF}$, because $\overline{AC} = 9in$, $\overline{DF} = 8 in$. <C is congruent to <F. $\overline{EF}$ must correspond to $\overline{BC}$. The triangles are congruent by the SAS Triangle

Congruence Theorem only when x = 4.

Step-by-step explanation:

From the figures given, ∆ABC and ∆DEF have an included corresponding angles measuring 30° each (<C and <F), and also a given corresponding side length of 9 in each (side AC and side DF). The other given as am expression, and hence the length is unknown. For these two ∆s to be considered congruent, using the SAS Triangle Congruence Theorem, we must have two sides and an included angle of ∆ABC equal to the corresponding sides of and an included angle of ∆DEF.

We already know that 1 of the given side corresponding side lengths are equal and also the include angles are equal, to find out what value of x that will make both unknown corresponding lengths equal, in other for the SAS to be true, set 2x equal to (x + 4) to solve for x.

Thus:

2x = x + 4

Subtract x from both sides

2x - x = 4

x = 4

Substituting x = 4 into 2x and x + 4 will give us equal lengths of 8 in respectively. Therefore, if x = 4, both triangles will be congruent based on the SAS Triangle Congruence Theorem.

The answer is:

$\overline{AC}$ is congruent to $\overline{DF}$, because $\overline{AC} = 9in$, $\overline{DF} = 8 in$. <C is congruent to <F. $\overline{EF}$ must correspond to $\overline{BC}$. The triangles are congruent by the SAS Triangle

Congruence Theorem only when x = 4.