Indicate whether the given information in the diagrams allows you to reach the given conclusion.  Triangle 1: Segment AP `` segment BP? (Yes or No)   Triangle 2: Segment PC `` segment AB?...

Indicate whether the given information in the diagrams allows you to reach the given conclusion. 

Triangle 1: Segment AP `` segment BP? (Yes or No)  

Triangle 2: Segment PC `` segment AB? (Yes or No)

Triangle 3: C lies on line PQ? (Yes or No)

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Expert Answers
embizze eNotes educator| Certified Educator

(1) AP=BP PC is an altitude of an isosceles triangle from the vertex; thus PC is also the angle bisector of the vertex, the median from the vertex, and the perpendicular bisector of AB. Yes.

(2) Not necessarily. We would need more information. True if angle A has measure about 63.43 degrees. No.

(3) No. There are many lines that can be drawn through the midpoint of the base and a point in the interior of the triangle that do not intersect the opposite angle. No.