Question
Construct a triangle similar to $\triangle\text{ABC}$ in which AB = 4.6cm, BC = 5.1cm, $\angle\text{A}=60^\circ$ with scale factor 4 : 5.
✓
Answer
Given that Construct a $\triangle\text{ABC}$ of given data, AB = 4.6cm, BC = 5.1cm and $\angle\text{A}=60^\circ$ and then a triangle similar to it whose sides are $\Big(4:5=\frac{4}{5}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$ We follow the following steps to construct the given
Step of construction:
Step I: First of all we draw a line segment AB = 4.6cm.
Step II: With A as centre draw an angle $\angle\text{A}=60^\circ.$
Step III: With B as centre and radius = BC = 5.1cm, draw an arc, intersecting the arc drawn in step II at C.
Step IV: Joins BC to obtain $\triangle\text{ABC}.$
Step V: Below AB, makes an acute angle $\angle\text{BAX}=60^\circ.$
Step VI: Along AX, mark off five points $A_1, A_2, A_3, A_4$ and $A_5$ such that $AA_1 = A_1A_2 = A_2A_3 = A_3A_4 = A_4A_5.$
Step VII: Join $A_5B.$
Step VIII: Since we have to construct a triangle each of whose sides is $\Big(\frac{4}{5}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$ So, we take four parts out of five equal parts on AX from point $A_4$ draw $A_4B || A_5B$, and meeting AB at B’.
Step IX: From B’ draw B'C' || BC, and meeting AC at C’. Thus, $\triangle\text{AB}'\text{C}'$ is the required triangle, each of whose sides is $\Big(\frac{4}{5}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$
Step of construction:
Step I: First of all we draw a line segment AB = 4.6cm.
Step II: With A as centre draw an angle $\angle\text{A}=60^\circ.$
Step III: With B as centre and radius = BC = 5.1cm, draw an arc, intersecting the arc drawn in step II at C.
Step IV: Joins BC to obtain $\triangle\text{ABC}.$
Step V: Below AB, makes an acute angle $\angle\text{BAX}=60^\circ.$
Step VI: Along AX, mark off five points $A_1, A_2, A_3, A_4$ and $A_5$ such that $AA_1 = A_1A_2 = A_2A_3 = A_3A_4 = A_4A_5.$
Step VII: Join $A_5B.$
Step VIII: Since we have to construct a triangle each of whose sides is $\Big(\frac{4}{5}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$ So, we take four parts out of five equal parts on AX from point $A_4$ draw $A_4B || A_5B$, and meeting AB at B’.
Step IX: From B’ draw B'C' || BC, and meeting AC at C’. Thus, $\triangle\text{AB}'\text{C}'$ is the required triangle, each of whose sides is $\Big(\frac{4}{5}\Big)^\text{th}$ of the corresponding sides of $\triangle\text{ABC}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
For what value of $k, -4$ is a zero of the polynomial $x^2 - x - (2k + 2)$?
→A bag contains 6 red balls and some blue balls. if the probability of a drawing a blue ball from the bag is twice that of a red ball, find the number of blue balls in the bag.
Find the ratio in which the y-axis divides the line segment joining the points (5, -6) and (-1, -4). Also, find the coordinates of the point of division.
Which of the following sequences are arithmetic progressions. For those which are arithmetic progressions, find out the common difference.
$12, 2, -8, -18, .....$
→$12, 2, -8, -18, .....$
Out of a group of swans, $\frac{7}{2}$ times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
→Two triangles are similar .Smaller triangle sides are $4\ cm ,5\ cm,6\ cm$ perimter of larger triangle is $90\ cm$ then find the sides of larger triangle.
→Find the lengths of the medians of a $\triangle\text{ABC}$ whose vertices are A(0, -1), B(2, 1) and B(2, 1) and C(0, 3).
→In an A.P., if the $5^{\text {th }}$ and $12^{\text {th }}$ terms are $30$ and $65$ respectively, what is the sum of first $20$ terms?
→Find the coordinates of a point A, where AB is a diameter of a circle with center C(2, -3) and the other end of the diameter is B(1, 4).