In Fig. 14.97, BE⊥AC. AD is any line from A to BC intersecting BE in H, P, Q and R are respectively the mid points of AH, AB and BC. Prove that ∠PQR = 90°
Answers
Given :
In ΔABC, Q and R are the mid points of AB and AC
QR || AC …………...(i) [mid point theorem]
In ΔABH,
Q and P are the mid points of AB and AH
QP || BH
QP || BE ……….... (ii) [mid point theorem]
But BE ⊥ AC therefore from eq (i) & (ii), we have
QP ⊥QR
Hence, proved ∠PQR = 90°
Hope this answer will help you…
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To Prove ∠PQR = 90°
Step-by-step explanation:
Given:
BE ⊥ AC
P is midpoint of AH
Q is the midpoint of AB
R is the midpoint of BC
Proof :
In ΔABC , as Q and R are the midpoints of AB and BC
∴ QR is parallel to AC (QR║AC) ............( 1 )
In ΔABH, as Q and P are the midpoints of AB and AH
∴QP ║BH .............................(2)
As BE ⊥ AC and from we equations (1) and (2)
we get QP ⊥QR
∴ ∠PQR = 90° , hence proved.
To Learn More......
1. In the given fig.,BE perpendicular AC. AD is any line from A to BC intersecting BE at H. P, Q and R are mid-points of AH, AB and BC respectively, then prove that angle PQR=90o.
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2. State and prove mid point theorem
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