Question

In a triangle PQR , PQ=8cm , QR=10cm , PR=12cm . If E, F and G are mid points of PQ, QR and
PR , find the length of EF and GE

Answer 1

GIVEN QUESTION :-

• In a triangle PQR , PQ=8cm , QR=10cm , PR=12cm . If E, F and G are mid points of PQ, QR and PR , find the length of EF and GE.

ANSWER

GIVEN :-

• In a triangle PQR

• PQ=8cm , QR=10cm , PR=12cm .

• E, F and G are mid points of PQ, QR and PR

TO FIND :-

• The length of EF and GE.

CONCEPT USED :-

MIDPOINT THEOREM :-

• The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

SOLUTION :-

Given that

• In ∆ PQR

• PQ = 8 cm

• QR = 10 cm

• PR = 12 cm

Now,

• In ∆ PQR

Since,

• E is the midpoint of PQ

and

• G is the midpoint of PR.

So,

• By Midpoint Theorem,

$\rm :\implies\:EG \: = \: \dfrac{1}{2} \times QR$

$\rm :\implies\:EG \: = \: \dfrac{1}{2} \times 10$

$\rm :\implies\: \boxed{ \bf \: EG \: = \: 5 \: cm}$

Again,

• E is the midpoint of PQ

and

• F is the midpoint of QR

So,

• By Midpoint Theorem,

$\rm :\implies\:EF \: = \: \dfrac{1}{2} \: PR$

$\rm :\implies\:EF \: = \: \dfrac{1}{2} \times 12$

$\rm :\implies\: \boxed{ \bf \: EF \: = \: 6 \: cm}$

Additional Information :-

Additional Information :- Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.