Geometry: An Interactive Journey to Mastery

Example 3
Prove that each diagonal in a rhombus bisects interior angles
of the rhombus. That is, in the diagram in Figure 14.2, prove
that x 1 = x 3 and x 2 = x 4.
Solution
The two triangles in the diagram are congruent by SSS. Thus, x 1 = x 3 and x 2 = x 4 because matching angles in
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Study Tip
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Work, instead, at being adept at reconstructing the basic proofs behind the facts and deducing what the
properties must be.
Pitfall
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1. The opposite sides of a quadrilateral are congruent. Prove that the
   TXDGULODWHUDOPXVWEHDSDUDOOHORJUDPͼ௘6HHFigure 14.3௘ͽ


2. For one pair of sides of a quadrilateral, edges are both congruent
   and parallel. Prove that the quadrilateral must be a parallelogram.
   ͼ௘6HHFigure 14.4௘ͽ

Comment: Feel free to use the results of Problems 1 and 2, and Example 1, throughout the remainder of this
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xx 13 xx 42

Figure 14.2

Problems

a

b b

a

Figure 14.3

a

a Figure 14.4