∆ABC yali DE||BC, DE = 3cm, BC=9cm matuu AD = 2cm adre AB =? Udaavestuu
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Answer:
AB =6cm
Step-by-step explanation:
Given: DE || BC, DE = 3cm, BC = 9cm, AD 2cm
To find: The length of AB
Solution: Since DE || BC, angle D angle B and angle E = angle C.
Angle A remains the same.
Now the AAA (angle-angle-angle) similarity theorem states that two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
So by AAA criteria, we see that triangle
ABC triangle ADE. ~
Since DE/BC = 3 cm/9 cm
⇒DE/BC=1/3
⇒ AD/AB = 1/3
⇒ AB = 3.AD
⇒AB = 3 x 2 cm
⇒AB = 6 cm
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