Construction of an Isosceles Triangle Triangle

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Question 6

Draw a circle with centre C and radius 3.4 cm. Draw any chord $\overline{AB}$. Construct the perpendicular bisector $\overline{AB}$ and examine if it passes through C.

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​​​​​​​Draw an isosceles triangle with each of equal sides of length 3 cm and the angle between them as ${45}^{\circ }$.

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Question 7

Draw a circle with centre C and radius 3.4 cm. Draw any chord $\overline{AB}$. Construct the perpendicular bisector $\overline{AB}$ and examine if it passes through C if $\overline{AB}$ happens to be the diameter.

Q. Draw $△CAR$ in which $CA=8cm,\angle A={60}^{\circ }$ and $AR=8cm$. Measure angle $C$. What kind of triangle is this ?

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Question 2

Draw a line segment of length 9.5 cm and construct its perpendicular bisector.

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In this figure, triangle ABC is right - angled at B. Given that AB = 9 cm, AC = 15 cm and D and E are the mid-points of the sides AB and AC respectively, calculate the area of $\Delta ADE$.

1. $13c{m}^2$

2. $12c{m}^2$

3. $13.5c{m}^2$

4. $14c{m}^2$

Q. Question 2
Construct the following and give justification :

A $\Delta PQR$, given that QR = 3cm, $\angle PQR={45}^{\circ }$ and QP – PR = 2cm.

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The angle of measures ${72}^{\circ }$ and ${144}^{\circ }$ are bisected to get 'a' and 'b' respectively.
What is the value of a+b in degrees?

1. 7.0 cm

2. 6.5 cm

3. 10.0 cm

4. 5.0 cm

Q. Construct an isosceles triangle $ABC$ such that
$AB=6cm,BC=AC=4cm.$ Bisect $\angle C$ internally and mark a point $P$ on this bisector such that $CP=5cm.$ Find the points $Q$ and $R$ which are $5$$cm$ from $P$ and also $5$$cm$ from the line $AB$.

Q. A pair of straight lines drawn through the origin forms an isosceles right triangle with the line $2x+3y=6$, then the lines and the area of the triangle thus formed is

1. $\begin{array}{c}x-5y=0\\ 5x+y=0\\ \Delta =\frac{36}{13}\end{array}$
2. $\begin{array}{c}3x-y=0\\ x+3y=0\\ \Delta =\frac{12}{17}\end{array}$
3. $\begin{array}{c}5x-y=0\\ x+5y=0\\ \Delta =\frac{13}{5}\end{array}$
4. None of these

Q. Construct an isosceles $△ABC,$ where base $AB=7cm$ and $\angle ABC={50}^o$. Also, find the measure of $\angle ACB$.

1. ${50}^0$
2. ${80}^o$
3. ${100}^o$
4. ${120}^o$

Q. Draw $△PQR$ with $PQ=4$ cm, $QR=3.5$ cm and $PR=4$ cm. What type of triangle is this?

Q. Then angle of elevation of a top of a tower (point B) from a point A on ground at horizontal distance $d$ from foot of the tower is ${45}^o$. Angle of elevation from a point C $30m$ vertically above point $A$ is ${30}^o$. Then the value of $d$ is

1. $15(3+\sqrt{3})$
2. $30(\sqrt{3}-1)$
3. $30(3+\sqrt{3})$
4. $15(\sqrt{3}+1)$

Q. Which is the last step in the process?

1. $1$
2. $2$
3. $3$
4. $4$

Q. Construct an isosceles triangle, given its base and base angle justify the construction.

Q. Construct an isosceles triangle in which the length of each of its equal sides is $6.5cm$ and the angle between them ${110}^o$.

Q. Construct a triangle $PQR$ in which $QR=6cm,\angle Q={60}^o$ and $PR-PQ=2cm$.

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Q. Construct an isosceles triangle whose base is $8cm$ and altitude $4cm$ and then draw a another triangle whose sides are $1\frac{1}{2}$ times the corresponding sides of the isosceles triangle.

Q. Construct an isosceles $△ABC$ such that base $AB=4.2cm$. base $angle={30}^o$.

Q. Construct an isosceles triangle ABC such that AB$=6$cm, BC$=$AC$=5$cm. Bisect $\angle$C internally and mark a point 'p' on the bisector such that CP$=5.5$cm. Find points Q and R which are $5$ cm from 'p' and also from the line AB.