ABC is a right triangle right angled at C. DE is perpendicular to AB. AD is 3cm, DC is 2cm and CB is 12cm. Prove that triangle ABC is congruent to triangle ADE and find the lenghts of AE and DE.
Answers
Answered by
1
BC = 12cm
AD = 3cm
And CD = 2cm
Now in ΔABC and ΔADE, we have
∠A = ∠A (common)
∠ACB = ∠AED = 90°
In ΔABC by pythagoras theorem
Now in similar triangle ABC and ADE, we have
AD/AB = DE/BC = AE/AC
= 3/13 = DE/12 = AE/5
= 3/13 = DE/12 and 3/13 = AE/5
= DE = 36/13cm and AE = 15/13 cm
Similar questions