Answer:
(a) AA Similarity using alternate interior angles
(b) 6.3
Explanation:
(a)
Triangles ABD and BDC have a given pair of congruent angles, angles ABD and BCD.
With parallel lines AB and DC and transversal BD, then alternate interior angles ABD and BDC are congruent.
Now we have two pairs of congruent corresponding angles, so by AA Similarity, triangles ABD and BDC are similar.
(b)
Triangles ABD and BDC are similar.
The ratios of the lengths of corresponding sides are equal.
AB/BD = AD/BC
4/6 = 4.2/BC
4BC = 6 × 4.2
BC = 6.3