Prove that if a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.

› Trigonometry › Prove that if a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.

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2 years ago

Given: △ ABC,DEparallel AB Prove:△ DEC~△ ABC

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chrisstapletonticketsbirminghamal Staff answered 2 years ago

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)

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