IF the angles of one triangle are respectively equal to the angles of the another triangle, prove that the ratio of their corresponding sides is the same as the ratio of their corresponding (i) medians (ii)angle bisectors (iii) altitudes.
Answers
Proved that the ratio of their corresponding sides is the same as the ratio of their corresponding (i) medians (ii)angle bisectors (iii) altitudes.
Step-by-step explanation:
let say ΔABC & ΔPQR
∠A = ∠P
∠B = ∠Q
∠C = R
=> ΔABC ≈ ΔPQR
=> AB/PQ = BC/QR = AC/PR
(i) medians
Lets draw AD & PS median
=> BD = CD = BC/2 & QS = RS = QR/2
BD/QS = (BC/2)/(QR/2) = BC/QR
=> AB/PQ = BD/QS & ∠B = ∠Q
=> ΔABD ≈ ΔPQS
=> AB/PQ = BD/QS
similarly we can show for other medians
(ii)angle bisectors
AD & PS are angle bisectors
=> ∠BAD = ∠A/2 ∠QPS = ∠P/2
=> ∠BAD = ∠QPS
∠B = ∠Q
=> ΔABD ≈ ΔPQS
=> AB/PQ = BD/QS
similarly we can show for other angle bisectors
(ii) altitudes.
AD & PS are altitudes.
=> ∠BDA= 90° ∠QSP = 90°
=> ∠BDA= ∠QSP
∠B = ∠Q
=> ΔABD ≈ ΔPQS
=> AB/PQ = BD/QS
similarly we can show for other altitudes.
Learn more:
if perimeter of the two similar triangles are the in the ratio 5 : 4 then ...
https://brainly.in/question/7633761
if the ratio of the corresponding sides of two similar triangles is 2:3 ...
https://brainly.in/question/8119105