Asked by Dari b
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
Answers
Answered by
GPT 3.5
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.
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.