Question
Construct an isosceles triangle in which: $XY = XZ, YZ = 5.5 \ cm$ and $\angle X = 60^\circ $
✓
Answer
In $\triangle XYZ,$
$XY = XZ ....($given$)$
$c \angle XZY = \angle XYZ ....(i)$
$\angle X = 60^\circ ....($given$)$
Now, $\angle X + \angle Y + \angle Z = 180^\circ $
$60^\circ + \angle Y + \angle Y = 180^\circ ....[$From $(i)]$
$2\angle Y = 120^\circ $
$\Rightarrow \angle Y = 60^\circ = \angle Z$
Steps:
$1.$ Draw $YZ = 5.5\ cm.$
$2.$ Construct $\angle YZP = 60^\circ $ and $\angle ZYQ = 60^\circ $
$3.$ Ray $ZP$ and $YQ$ meet at $x.$
Thus, $\text{XYZ}$ is the required triangle.
$XY = XZ ....($given$)$
$c \angle XZY = \angle XYZ ....(i)$
$\angle X = 60^\circ ....($given$)$
Now, $\angle X + \angle Y + \angle Z = 180^\circ $
$60^\circ + \angle Y + \angle Y = 180^\circ ....[$From $(i)]$
$2\angle Y = 120^\circ $
$\Rightarrow \angle Y = 60^\circ = \angle Z$
Steps:
$1.$ Draw $YZ = 5.5\ cm.$
$2.$ Construct $\angle YZP = 60^\circ $ and $\angle ZYQ = 60^\circ $
$3.$ Ray $ZP$ and $YQ$ meet at $x.$
Thus, $\text{XYZ}$ is the required triangle.
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
In $\triangle ABC$,Find the sides of the triangle, if:
→- $AB = ( x - 3 ) \ cm, BC = ( x + 4 ) \ cm$ and $AC = ( x + 6 ) \ cm$
- $AB = x \ cm, BC = ( 4x + 4 ) \ cm$ and $AC = ( 4x + 5) \ cm$
Four identical cubes are joined end to end to form a cuboid. If the total surface area of the resulting cuboid as $648\ m^2$; find the length of the edge of each cube. Also, find the ratio between the surface area of the resulting cuboid and the surface area of a cube.
→If $V = pr^2h$ and $S = 2pr^2 + 2$prh, then express $V$ in terms of $S, p$ and $r.$
→Arrange the following rational numbers in ascending order.$\frac{4}{5}, \frac{6}{7}$ and $\frac{7}{10}$
→A shopkeeper fixes the selling price of his goods at $60\%$ above the cost price. He sells half of this stock at this price, a quarter of his stock at a discount of $25\%$ on the original selling price, and the rest at a discount of $50\%$ on the original selling price. Find the gain percent altogether.
→→
Use graph paper for this question. Take $2 \ cm = 1$ unit on both the axes.$(i)$ Draw the graphs of $x + y + 3 = 0$ and $3x - 2y + 4 = 0$. Plot only three points per line.$(ii) $Write down the coordinates of the point of intersection of the lines.$(iii)$ Measure and record the distance of the point of intersection of the lines from the origin in $cm.$
→Construct a rectangle $\text{ABCD}$, when $AD = 3.2\ cm$ and diagonal $BD = 5.5\ cm$. Measure $CD.$
→The sum of the digits of a two digit number is $7$. If the digits are reversed, the new number decreased by $2,$ equals twice the original number. Find the number.
→Given two equal chords $AB$ and $CD$ of a circle with center $O$, intersecting each other at point $P.$Prove that:$(i) AP = CP;(ii) BP = DP$
→