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arsen [322]
2 years ago
11

50 points Prove and find the measurement?

Mathematics
2 answers:
frez [133]2 years ago
8 0

Answer:

1) they are similar by AAA postulate

2) 9.6 cm

Explanation:

Triangles CAB and CED are similar

because:

1) both have the same angle C

(vertically opposite angles)

2) Angle A = Angle E

(alternate angles)

3) Angle B = Angle D

(alternate angles)

CA/CE = AB/ED

10/8 = 12/DE

DE = 12 × 8/10

DE = 9.6 cm

nydimaria [60]2 years ago
7 0

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

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