Using ruler and compasses only- construct a - A B C- given base B C-7 cm - - A B C-60- and A B-A C-12 cm-

We are asked to construct a triangle ABC in which BC = 7 cm, ∠B = 60° and AB nbsp;+ AC = 12 cm We will follow the following algorithm for the construction ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Given Base(BC), Base Angle(ABC) and AB-AC

Using ruler a...

Question

Using ruler and compasses only, construct a ΔABC, given base BC = 7 cm, ∠ABC = 60° and AB + AC = 12 cm.

Open in App

Solution

We are asked to construct a triangle ABC in which BC = 7 cm, ∠B = 60° and AB + AC = 12 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of length 7 cm.

STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.

STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.

STEP4: Draw BM and produce it to P.

STEP5: From BP, cut BR = 12 cm.

STEP6: Draw segment RC.

STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.

STEP8: Draw AC.

ΔABC is the required triangle.

Suggest Corrections

Similar questions

Using ruler and compasses only, construt a $△ A B C,$ given base BC = 7 cm, $△ A B C = 60^{\circ}$ and AB + AC = 12 cm.

Q. Using ruler and compasses only, construct a Δ ABC from the following data:
AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Using ruler and compasses only, construct a $△$ ABC, from the following data :

AB + BC + CA = 12 cm, $∠ B = 45^{\circ} a n d ∠ C = 60^{\circ}$ .

Q. Using ruler and compasses only, construct a

△ A B C

having given

∠ A B C = 60^{0}, ∠ A C B = 45^{0}

and the perpendicular from

A

B C

equal to

2.5

cm. The length of

A B

Q. Using ruler and compasses only, construct a triangle

A B C

such that

B C = 6

cm, angle

B = 60^{0}

and the length of the perpendicular from vertex

A

to the base

B C = 25

cm.

Join BYJU'S Learning Program