Question

Triangle ABC is congruent to triangle ADC by the SSS criterion. What is the value of x? Triangle ABC shares a common side AC with triangle ADC, forming a kite shape. Segments AB, BC, CD, and DA are labeled 12, x + 12, 2x - 6, and 12 respectively. Select the correct answer.

1) 18
2) 12
3) 6
4) 2

Answer 1

To find the value of x, we can set up an equation based on the SSS criterion. By substituting the corresponding sides of triangle ABC and triangle ADC, we can solve for x.

Step-by-step explanation:

To determine the value of x, we can set up an equation based on the SSS criterion. According to the SSS criterion, if two triangles have the same corresponding sides, then they are congruent. In this case, triangle ABC is congruent to triangle ADC, so AB = 12, BC = x + 12, and CD = 2x - 6.

Since triangle ABC is congruent to triangle ADC, their corresponding sides are equal. Therefore, we can set up the equation AB = CD.

Substituting the given values, we have 12 = 2x - 6.

Now we can solve for x:

12 + 6 = 2x

18 = 2x

Dividing both sides by 2:

x = 9

Therefore, the value of x is 9.