Question

50 Points + 50 points +

1. Find the measurements of DE

2. Find the lengths of BC EC

3. Find the 1) width, 2) height only workings.

Do not need perimeter or area for question 3. So just need exact workings

for 1, 2 and 3 width and height parts.... if answering questions.

Answer 1

see below

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