Understanding Similar Triangles

What is the main goal when analyzing the two triangles in the problem?

• To calculate the perimeter of the triangles

• To identify the type of triangles

• To determine if the triangles are similar

• To find the area of the triangles

Which theorem is NOT mentioned as a method to prove triangle similarity?

• Angle-Angle (AA)

• Angle-Side-Angle (ASA)

• Side-Angle-Side (SAS)

• Side-Side-Side (SSS)

What condition allows the use of alternate interior angles in this problem?

• The lines are parallel

• The triangles are right-angled

• The triangles are congruent

• The triangles have equal sides

What is the proportion set up to solve for x in the problem?

• x - 3 is to x + 18 as 4 is to 16

• x + 3 is to x + 18 as 16 is to 4

• x - 3 is to x - 18 as 16 is to 4

• x + 3 is to x - 18 as 4 is to 16

What is the first step in solving the equation after setting up the proportion?

• Divide by 12

• Cross multiply the terms

• Subtract 4x from both sides

• Add 48 to both sides

What is the result of 4 times (x + 18) in the equation?

• 4x + 48

• 4x + 64

• 4x + 18

• 4x + 72

What is the simplified form of the equation after applying the distributive property?

• 4x - 32 = 16x - 48

• 4x + 72 = 16x - 48

• 4x + 64 = 16x - 48

• 4x - 64 = 16x + 48

What operation is performed after subtracting 4x from both sides?

• Divide by 12

• Add 48 to both sides

• Subtract 48 from both sides

• Multiply by 12

What is the final value of x after solving the equation?

• 9.3

• 10

• 12

• 11.2

Why can't the value of x be 10 in the final calculation?

• Because 12 times 10 is 100

• Because 12 times 10 is 120

• Because 12 times 10 is 112

• Because 12 times 10 is 110