ABCD is a parallelogram. AB is divided at P and CD at Q such that AP : PB is 3 : 2 and CQ : QD is 4 : 1. if PQ meets AC at R, prove that AR= 3/7 AC ?
SHARE
Answers
Answered by
6
Solution:
A Parallelogram A B CD in which , two points P and Q lies on side AB and CD Such that AP: PB=3:2 and C Q:Q D=4:1.Diagonal AC is intersected by Segment P Q at Point R.
Consider two triangles in the parallelogram ,ΔA RP and Δ C R Q
∠ARP=∠CRQ→→[Vertically Opposite Angles]
∠PAR=∠RCQ→→[ Alternate Interior Angles]
ΔA RP ~ Δ C R Q→→[AA Similarity]
Keep in Mind , when two triangles are similar , their corresponding sides are proportional.
AB= CD→→ [Opposite sides of a Parallelogram are equal]
Let AP and PB be 3 k and 2 k respectively.and CQ and QD be 4 x and x respectively.
3 k + 2 k = 3 x + 2 x
5 k= 5 x
k = x
Attachments:
Similar questions
English,
6 months ago
Social Sciences,
6 months ago
Computer Science,
6 months ago
Chemistry,
1 year ago
Science,
1 year ago
English,
1 year ago
Biology,
1 year ago