4.2.1 Triangle Congruence: SSS and SAS (continued)
In this example, m ∠ E , EF , and DE are represented by expressions. m ∠ E = (7 x + 2)°
EF = 5 x + 1 DE = 3 x − 2
To show that the triangles are congruent for the given value of the variable, x = 4, first substitute 4 into each expression and simplify. m ∠ E = (7(4) + 2)° = 30° Therefore, m ∠ B = m ∠ E , BC = EF , and AB = DE . So, by the definition of congruence, each of these pairs of sides is congruent and the included angles are congruent. Since two sides and the included angle of △ ABC are congruent to two sides and the included angle of △ DEF , the two triangles are congruent by SAS. EF = 5(4) + 1 = 21 DE = 3(4) − 2 = 10 It is given that the two lines are parallel in this example. So, consider the theorems related to parallel lines, such as the Alternate Interior Angles Theorem. The Alternate Interior Angles Theorem states that if two lines are parallel and cut by a transversal, then the pairs of alternate interior angles are congruent. In this figure, ∠ DAB and ∠ ADC are a pair of alternate interior angles. Therefore, ∠ DAB ≅ ∠ ADC .
Example 4 Proving Triangles Congruent
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