Math, asked by saundarya35, 8 months ago

draw a triangle PQR where angles are in the ratio 1:2:3. Draw triangle ABC similar to triangle PQR whose sides are 1/3 times the sides of the triangle PQR

Answers

Answered by AditiHegde

A triangle PQR with angles in the ration 1:2:3 are given by 30°, 60°, 90°.

we know that, sum of angles in triangle =180°
given ration of angles = 1:2:3
let the angles be =x
then the ratio is given by,
x+2x+3x=180°
6x=180
x=30°
2x=60°
3x=90°
Now,
The triangle PQR is similar to triangle ABC, with the sides 1/3 times the sides of the triangle PQR.
If side of triangle PQR, that is, QR=6cm, then the side of triangle ABC, that is ,BC=2cm.

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Answered by amitnrw

Step-by-step explanation:

draw a triangle PQR where angles are in the ratio 1:2:3.

∠P : ∠Q = ∠R ::: 1 : 2 : 3

∠P = y

=> ∠Q = 2y

=> ∠R = 3y

y + 2y+ 3y = 180°

=> 6y = 180°

=> y = 30°

∠P = 30° , ∠Q = 60° & ∠R = 90°

Step 1 : Draw a line segment of any length PQ

Step 2 : Draw an angle of 30° at P using Protector and draw a Ray Starting from P

Step 3 : Draw an angle of 30° at Q using Protector and draw a Ray Starting from Q

Step 4 : Mark intersection point of rays drawn in step 2 & 3 as R

Δ PQR is constructed

To Draw Δ ABC ≈ Δ PQR whose sides ar 1/3 times of ΔPQR

Step 1 : Draw an acute angle at PQ

Step 2 : Using compass take three points on angle drawn at equal distance consecutively

Step 3 : join 3rd point with Q as straight line using ruler

Step 4 :Using set square draw a line parallel to drawn in step 3 passing through 1st point and intersecting PQ at S

Step 5 : using compass measure PS

Step 6 : Draw a line segment AB = PS

Step 7 : Draw an angle of 30° at A using Protector and draw a Ray Starting from A

Step 8 : Draw an angle of 30° at B using Protector and draw a Ray Starting from B

Step 9 : Mark intersection point of rays drawn in step 7 & 8 as C

Δ ABC is constructed

Learn more:

Construct the triangles with the measurement given in the following ...

https://brainly.in/question/13801010

Triangle pqr pq=8cm qr=7.5CM triangle pqr=85 degrees - Brainly.in

https://brainly.in/question/13721368

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