4.1.3 Congruent Triangles (continued)
The figure from the previous example is used again in this example. It is given that △ ABD ≅ △ CBD , ∠ CBD is a right angle, and m ∠ A = 31.4°. Make a plan for finding m ∠ BDC . Notice that the measures of two angles in △ ABD are known. Therefore, the Triangle Sum Theorem can be used to find the measure of the third angle, ∠ BDA . The two triangles are congruent, so their corresponding angles must also be congruent. The angle that corresponds with ∠ BDA is ∠ BDC . So, since corresponding angles of congruent triangles are congruent, ∠ BDA ≅ ∠ BDC and by the definition of congruence, m ∠ BDA = m ∠ BDC . Start this proof by listing all of the given information in the statements and by noting all of the given information on the figure. Now consider the conclusion to be proven: △ ACD ≅ △ ACB . One way to show that two triangles are congruent is by showing that all of their corresponding parts are congruent. Showing that all of the corresponding parts of two triangles are congruent means showing that three pairs of angles are congruent and that three pairs of sides are congruent. There are two important facts to remember for this proof. The first is that a segment’s midpoint divides a segment into two congruent parts (definition of midpoint). The second is that if two triangles share a side, that side is congruent to itself (the Reflexive Property of Congruence).
Example 3 Proving Triangles Congruent
208
Made with FlippingBook - Online magazine maker