Congruence vocabulary review

​We can prove that two triangles are congruent if we know that two angles of one triangle and the side between those two angles, are respectively equal to the two angles and the side between the angles of another triangle, then the two triangles will be congruent to each other by ASA rule.

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​When we know two sides and an angle between the sides we know that two triangles are congruent.

​We can prove that two triangles are congruent if they have three pairs of congruent sides.

The Perpendicular Bisector Theorem 

states that a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment.

B is on the perpendicular bisector of AC if and only if AB≅BC

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Since UV=VW=54, V is equidistant from the endpoints of UW. Therefore, V lies on the perpendicular bisector of UW by the Perpendicular Bisector Theorem.

Since V is on the perpendicular bisector of UW and ∠VXW is a right angle, VX is the perpendicular bisector of UW.

So, UX=WX=35 and UW=2(35)=70.