Question

Z A I + 5 4x - 3 3r-1 2x + 1 What value of x makes ASTW - AXYZ? s 3 + 1 T 4r-5 x = 2 X = 3 X=4 X=1

Answer 1

Here, we have two congruent triangles.

Given:

ST = 3x - 1 XY = 4x - 5

SW = 3x + 1 XZ = 4x - 3

TW = 2x + 1 YZ = x + 5

Since triangle STW and triangle XYZ are congruent, they have exactly the same corresponding sides.

To find the value of x, equate the corresponding sides and evaluate.

ST = XY

SW = XZ

TW = YZ

Take one of the corresponding sides.

We have:

ST = XY

3x - 1 = 4x - 5

Subtract 4x from both sides:

3x - 4x - 1 = 4x - 4x - 5

-x - 1 = -5

Add 1 to both sides:

-x - 1 + 1 = -5 + 1

-x = -4

Divide both sides by -1:

`\begin{gathered} (-x)/(-1)=(-4)/(-1) \\ \\ x=4 \end{gathered}`

Therefore, the value of x that makes ΔSTW ≅ ΔXYZ is 4

ANSWER:

x = 4