contestada

Ellen has property whose boundary lines form a triangle, as shown in the diagram. Her house lies at Vertex A and she is going to put a bunkhouse for the ranch hands somewhere along segment BC. She wants the placement to be such that CA/CD=B/A. What must be true about segment AD so that the proportion CA/CD=BA/BD holds

Respuesta :

Given that in a ΔABC, Ellen house lies at vertex A and bunkhouse is put somewhere along BC, let it be D.

Please refer the diagram attached.

We are also given that D must be placed such that [tex]\frac{CA}{CD}= \frac{BA}{BD}[/tex] holds true.

Let us re write the above equation such that CD and BD lie on one side.

That is [tex]\frac{CA}{BA}= \frac{CD}{BD}[/tex]

Which is nothing but angle bisector theorem.

Hence AD must bisect the angle A then only the given condition will hold true.

Ver imagen ColinJacobus

Answer:

D) Segment AD must bisect ∠A

Step-by-step explanation:

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