Answer:
see below
Step-by-step explanation:
Angle ACE = DCE since they are vertical angles
Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles
Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles
When all three angles are equal, the triangles are similar.
We can use ratios to find DE
DE CE
------- = ----------
AB AC
DE 8
------- = ----------
12 10
Using cross products
10 DE = 8*12
10 DE = 96
Divide by 10
DE = 9.6
2nd problem
Angle ADE is congruent to ABC because corresponding angles are conguent when parallel lines cut by a transversal
Angle AED is congruent to ACB because corresponding angles are conguent when parallel lines cut by a transversal
Angle A equals angle A by the reflexive property
When all three angles are equal, the triangles are similar.
We can use ratios to find BC
AD DE
------- = ----------
AB BC
8 5
------- = ----------
8+6 BC
Using cross products
8 BC = 5 (14)
8 BC =70
Divide each side by 8
BC =8.75
We can use ratios to find EC
AD AE
------- = ----------
AB AC
8 4.2
------- = ----------
8+6 4.2+EC
Using cross products
8 (4.2+EC) = 4.2*14
33.6 +8EC = 58.8
Subtracting 33.6
8EC =25.2
Dividing by 8
EC =3.15
