Mathematics
In the adjoining figure, AB = AC. If PM ⊥ AB and PN ⊥ AP, show that PM × PC = PN × PB.
Similarity
14 Likes
Answer
Considering △PNC and △PMB,
∠PNC = ∠PMB (Both are equal to 90°)
∠NCP = ∠PBM (As AB = AC)
Hence by AA axiom △PNC ~ △PMB.
Since, triangles are similar so ratio of their corresponding sides will be equal.
Hence, proved that PC × PM = PN × PB.
Answered By
11 Likes
Related Questions
In the figure (2) given below, medians BE and CF of a △ABC meet at G. Prove that :
(i) △FGE ~ △CGB
(ii) BG = 2GE
In the adjoining figure, ∠1 = ∠2 and ∠3 = ∠4. Show that PT × QR = PR × ST.
In the figure (1) given below, ∠AED = ∠ABC. Find the values of x and y.
In the given figure, P is a point on AB such that PB : AP = 3 : 4 and PQ || AC.
(i) Calculate PQ : AC.
(ii) If AR ⊥ CP, QS ⊥ CB and QS = 6 cm, calculate the length of AR.