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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(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.**

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