ABC is an eqilateral TRIANGLE. IF P AND Q ARE TTHE MID POINTS OF AB AND AC RESPECTIVELY AND PQ IS 3CM THEN THE VALUE OF PA AND AQ IS
Answers
On joining P and Q, PQ line will be parallel to line BC
By mid point theorm
1/2 of BC =PQ
BC= 2 PQ
BC=6 cm
As ABC is an equilatral Δ then AB=BC=CA
therefor P is mid point of AB ,Similarly Q is mid point of AC
PA=AQ=6/2=3cm
- The value of PA is equal to 3 cm .
- The value of AQ is also equal to 3 cm .
Given :-
- ABC is an eqilateral triangle .
- P and Q are the mid points of side AB and AC respectively .
- PQ = 3 cm .
Concept used :-
- Length of all sides of an eqilateral triangle are equal in measure .
- Mid point theorem :- The line segment joining the midpoint of two sides of a triangle is parallel and half of the length of the third side .
Solution :-
from given data we have,
→ AP = PB { since P is mid point of AB }
→ AQ = QC { since Q is mid point of AC }
Now, BC is third side of the ∆ABC .
So,
→ PQ = (1/2)•BC { By mid point theorem }
→ BC = 2•PQ
putting given value of PQ as 3 cm,
→ BC = 2 × 3
→ BC = 6 cm .
then,
→ AB = AC = BC = 6 cm { All sides of an eqilateral triangle are equal in measure }
therefore,
→ PA = (1/2)•AB { since P is mid point of AB }
→ PA = (1/2) × 6
→ PA = 3 cm (Ans.)
and,
→ AQ = (1/2)•AC { since Q is mid point of AC }
→ AQ = (1/2) × 6
→ AQ = 3 cm (Ans.)
Learn more :-
In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .
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