Given : triangle ABC ~ triangle XYZProve: Area abc/ Area xyz = AC^2/ XZ ^2

1. Through B and Y, draw lines perpendicular to AC and XZ, respectively, intersecting AC at D and XZ at W 1. Through a point there is one and only one perpendicular to a given line2. BD and YW are altitudes of triangle ABC and triangle XYZ respectively2. Definition of an altitude of a triangle3. Area of ABC=1/2(AC)(BD) ; Area of XYZ = (XZ)(YW)3. Definition of an area of a triangle4. Triangle ABC ~ Triangle XYZ4. Given5. BD/YW=AC/XZ5. In a pair of similar triangles, the lengths of the altitudes drawn from corresponding vertices are in the same ratio as the lengths of any corresponding sides6. AC(BD)/1/2 (XZ)(YW)= 1/2 AC^2/ XZ^2 6. MPE 7. Area of ABC/ Area of XYZ = 1/2 AC^2/ XZ^27. SPE8. Area of ABC/ Area of XYZ = AC^2/XZ^28. Division