Prove that if a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.
Given: △ ABC,DEparallel AB
Prove:△ DEC~△ ABC

1 Answers

Best Answer

Step 1
Given,
To prove: △ DEC~△ ABC
Step 2
Statements Reasons
1.△ ABC,DE ∥ AB - Given
2.∠A=∠CDE and ∠B=∠DEC - 2. If two parallel lines are cut by a transversal, then the corresponding angles are equal
3.△ DEC~△ ABC - 3.If two angles of one triangle are equal respectively to two angles of another, then the triangles are ~ilar. (AA)