Construct a right-angled triangle whose perimeter is equal to $10\ cm$ and one acute angle equal to $60^o$.
Given:
A right-angled triangle whose perimeter is equal to $10\ cm$ and one acute angle equal to $60^o$.
To do:
We have to construct the given triangle.
Solution:
Steps of construction:
(i) Draw a line segment $PQ = 10\ cm$.
(ii) At $P$, draw a ray $PX$ making an angle of $90^o$ and at $Q, QY$ making an angle of $60^o$.
(iii) Draw the angle bisectors of $\angle P$ and $\angle Q$ meeting each other at $A$.
(iv) Draw the perpendicular bisectors of $AP$ and $AQ$ intersecting $PQ$ at $B$ and $C$ respectively,
(v) Join $AB$ and $AC$.
Therefore,
$\triangle ABC$ is the required triangle.
Related Articles
- Construct a triangle whose perimeter is $6.4\ cm$, and angles at the base are $60^o$ and $45^o$.
- Construct a right-angled triangle whose hypotenuse is $6\ cm$ long and one of the legs is $4\ cm$ long.
- Determine the measure of each of the equal angles of a right angled isosceles triangle.OR$ABC$ is a right angled triangle in which $\angle A = 90^o$ and $AB = AC$. Find $\angle B$ and $\angle C$.
- Construct the quadrilateral ABCD. AB is equal to 4.5 cm, BC is equal to 5.5 cm, CD is equal to 4 cm, AD is equal to 6 cm and AC is equal to 7 cm
- Can a triangle have:All angles equal to $60^o$?Justify your answer.
- Construct an isosceles right-angled triangle $ABC$, where $m\angle ACB = 90^{\circ}$ and $AC = 6\ cm$.
- In a $\triangle ABC, \angle A = x^o, \angle B = 3x^o and \angle C = y^o$. If $3y - 5x = 30$, prove that the triangle is right angled.
- If in two right triangles, one of the acute angles of one triangle is equal to an acute angle of the other triangle, can you say that the two triangles will be similar? Why?
- If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right triangle.
- In triangle ABC, angle A is equal to 44°. If AB is equal to AC, find angle B and angle C.
- $ABC$ is a right angled triangle in which $\angle A = 90^o$ and $AB = AC$. Find $\angle B$ and $\angle C$.
- Construct the right angled $∆PQR$, where $m\angle Q = 90^{\circ},\ QR = 8cm$ and $PR = 10\ cm$.
- Construct a right triangle $ABC$ whose base $BC$ is $6\ cm$ and the sum of hypotenuse $AC$ and other side $AB$ is $10\ cm$.
- Using ruler and compasses only, construct a $\triangle ABC$, from the following data:$AB + BC + CA = 12\ cm, \angle B = 45^o$ and $\angle C = 60^o$.
- Construct a $\vartriangle ABC$ in which $AB\ =\ 6\ cm$, $\angle A\ =\ 30^{o}$ and $\angle B\ =\ 60^{o}$, Construct another $\vartriangle AB’C’$ similar to $\vartriangle ABC$ with base $ AB’\ =\ 8\ cm$.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies