Question

The length of each side of an equilateral . ABC is 8cm. Pand Q are the mid points of the sides AB
and AC respectively. Find the value of the length PQ and Z APQ.
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Answer 1

Answer:

PQ = 4 cm and angle APQ=60^

Step-by-step explanation:

given an equilateral triangel, ABC of length = 8cm

Rightarrow angle A= angle B= angle C=60^ ---

1)

also, given that P and Q are midpoints of AB and AC resply,

=> PQ || c-- (2)

(by the property, the line joining the midpoints of any two sides of a triangle is parallel to the third side.)

if considered AB is the transversal of the parallel lines, PQ and BC, Rightarrow angle B= angle P (3) (corresponding angles

are equal )

similarly, taken AC as the transversal of the parallel lines, PQ and BC,

Rightarrow angle C= angle Q

4) (corresponding angles

are equal )

so, by (1), (3) and (4),

Rightarrow angle P= angle Q=60^

ie., angle APQ=60^ \& angle AQP=60^

the same can be considered as,

in triangle APQ , angle A= angle P= angle Q=60^

=> triangle APQ is an equilateral triangle -(6)

so, the soln is PQ = 4 cm and angle APQ=60^

given P is midpoint of AB( 8cm), so, AP=AB/2= 4cm

ie., AP=AQ=PQ=4cm by (6)

Step-by-step explanation:

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