Question

Geometry math question

Answer 1

Hi!

You can find the value of x by the fact that as triangle CBE and CKE are congruent. The reason you can see the triangles are congruent is because of the AAS congruence postulate, where if two angles are the same and a non included side are congruent, the triangles are similar. In this case, angle CKE and angle CBE, are congruent, and CEB and CEK are congruent as well. (They're marked out as congruent.) The line CE is congruent to the other CE in the other triangle, because they are the same line.

Since you know the triangles are congruent, according to CPCTC (corresponding parts in congruent triangles are congruent), and line CK is congruent to line CB, line CK is congruent to CB, and has the same measure.

Therefore, you can set the measures of CB (5x - 3) and CK (3x + 1) equal to another and solve for x.

5x - 3 = 3x + 1

5x -3 + 3 = 3x + 1 + 3

5x = 3x + 4

5x - 3x = 3x - 3x + 4

2x = 4

2x / 2 = 4/2

x = 2, or choice C.

Hope this helps!

Answer 2

Make the side lengths equal to each other in an equation. They are equal because they are corresponding sides to congruent triangles.

5x - 3 = 3x + 1

Subtract 3x from both sides.

2x - 3 = 1

Add 3 to both sides.

2x = 4

Divide both sides by 2.

x = 2

C) 2