show that triangle ABC and xyz in the diagram below are similar if AB is equal to 12 cm XY is equal to 8 cm and XC is equal to 6 cm find BC

1 answer

To show that triangle ABC and triangle XYZ are similar, we need to show that all corresponding angles are equal and that the corresponding sides are in proportion.

Given:
AB = 12 cm
XY = 8 cm
XC = 6 cm

Since AB = XY, ∠A = ∠X (corresponding angles are equal by SAS).

Also, XC = 6 cm = 0.5*AB
Therefore, BC = 0.5*BC = 0.5*12 = 6 cm

Therefore, triangle ABC and triangle XYZ are similar by the SAS similarity criterion.

And BC = 6 cm.