Question
Construct an isosceles right-angled triangle, having hypotenuse= 8 cm. Draw its lines of symmetry.

Answer


Steps of construction:
(i) Draw a line segment BC= 8 cm
(ii) Draw its perpendicular bisector whidi intersects BC at D. With Das centre and BD or CD as radius, draw a semi-circle.
(iii) Produce the perpendicular bi sector of BC which intersects the ci rel e at A.
(iv) Join AB and AC. Triangle ABC is the required isosceles right-angled triangle.
The perpendicular bisector of hypotenuse BC is the line of symmetry.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

$(3x + 5)$ is a factor of the polynomial $(a – 1)x^3 + (a + 1)x^2 – (2a + 1)x – 15$. Find the value of ‘a’, factorise the given polynomial completely.
A( 4, 1 ), B(2,3) and C( 5,6) are the vertices of a figure which is symmetrical about x=7. Complete the figure and give the geometrical name of the figure if any.
Three circles touch each other externally. A triangle is formed when the centres of these circles are joined together. Find the radii of the circle, if the sides of the triangle formed are 6 cm, 8 cm and 9 cm
Ramesh had Rs $100$ shares of 'Bihar Steel' paying $8\%$ dividend. He sold them at a market price of Rs $130$ and invested the proceeds in buying Rs $50$ shares of 'Jindal steel' available at Rs $75$ and paying $12\%$ dividend. He thus increased the annual income by Rs $360.$ How many shares did Ramesh sell?
Tarun invested Rs 24,000 and Rs 30,000 in buying Rs 100 at par shares of 'Vam Organics' and 'Hero Honda' which later declared dividend of 12% and 15% respectively. After collecting the dividends Tarun sold the shares as their prices had fallen by Rs 5 and Rs 10 respectively. Find Tarun's earnings from the above transactions.
Bisectors of angles $A, B$ and $C$ of a triangle $A B C$ intersect its circumcircle at $D, E$ and $F$ respectively. Prove that the angles of $\triangle D E F$ are $90^{\circ}-\frac{ A }{2}, 90^{\circ}-\frac{ B }{2}$ and $90^{\circ}-\frac{ C }{2}$ respectively.
A man standing on a cliff observes a ship at an angle of depression of the ship is 30°, approaching the shore just beneath him. Three minutes later, the angle of depression of the ship is 60°. How soon will it reach the shore?
From the top of a cliff, $60$ metres high, the angles of depression of the top and bottom of a tower are observed to be $30^\circ$ and $60^\circ$ . Find the height of the tower.
Construct a frequency polygon without using a histogram for the following frequency distribution :
Class Mark 10 15 20 25 30 35 40
Frequency 4 20 40 45 30 25 5
If $a: b=c: d$, then prove that $\frac{a^2+c^2}{b^2+d^2}=\frac{a c}{b c}$