Answer:
1. △ABC and △PQR are isosceles triangle since its two sides are congruent. Hence in △ABC, ∠B can be determined as ∠B = 180 - 2(70) = 40°. From this we can conclude that ∠B ≅ ∠Q. Also, since the two triangles are isosceles triangles, the ratio of their corresponding sides are equal. Therefore, △ABC∼△PQR using SAS Similarity.
2. Given that BE and CD are parallel, ∠AEB ≅ ∠ADC and ∠ABE ≅ ∠ACD since they are corresponding angles. Hence, we can conclude that △ABE∼△ACD by AAA Similarity.
[tex]\frac{x}{3} =\frac{x+6}{3+4.5}[/tex]
[tex]7.5x=3x+18[/tex]
[tex]x=\frac{18}{7.5-3} =4[/tex]
[tex]BE=x=4[/tex]
[tex]CD=x+6=4+6=10[/tex]
