Draw and label a diagram. List, in terms of the diagram, what is given and what is to be proved. then write a two-column proof.

Question

1. In an isosceles triangle, if a segment is drawn from the vertex of the angle between the congruent sides to the midpoint of the opposite side, then congruent triangles are formed.
2. If a line perpendicular to line AB passes through the midpoint of line AB, and segments are drawn from any other point on that line to A and B, then two congruent triangles are formed.

Answer 1

1. Triangle is ABC. Line is drawn from B to midpoint D of opposite side.

Two triangles are formed: ABD and CBD.

BD = BD reflexive property

AB = CB definition of isosceles triangle

AD = CD definition of midpoint

ABD = CBD SSS

2. D is perpendicular bisector of AB. C is point on AB drawn to A and B.

ADC and DBC are two triangles that are formed

CD = CD reflexive property

AD = DB definition of midpoint

AC = BC any point on a perpendicular bisector of a segment is equidistant from the endpoints of that segment

ADC = DBC SSS