Isosceles Triangle

Q. if a perpendicular is drawn from vertex of the right angle of a triangle to hypotenuse then triangles on both side of a perpendicular are similar to the whole tringle and to each oth er.

Q.

Side BC of a triangle ABC has been produced to a point D such that $\angle ACD={120}^{\circ }.$ If $\angle B=\frac{1}{2}\angle A,$ then $\angle A$is equal to

Q. In a triangle ABC, AB = AC then $\angle B=$ ______.

1. $\angle A$
2. $\angle C$
3. ${180}^0-\angle C$
4. ${180}^0-\angle A$

Q.

If a side of an equilateral triangle is $xcm$, then its perimeter will be :

1. $x$

2. $2x$

3. $3x$

4. $4x$

Q. 31. prove that in a triangle, angle opposite to the longest side is greater than 2/3 of right angle

Q.

If ABC is a triangle , AB = AC, and AB = BC then ΔABC

1. Isosceles triangle

2. Right triangle

3. Equilateral triangle

4. Scalene triangle

Q. In triangle ABC, $\angle ABC={90}^{\circ }$ and P is a point on AC such that $\angle PCB=\angle PBC$, then PA = __

1. PC
2. PB
3. 2 PC
4. 2 PB

Q. If ABC is a triangle such that AB = BC and $\angle B={60}^{\circ }$, then what is the $\angle A$?

1. $\angle A={60}^{\circ }$
   
2. $\angle A={70}^{\circ }$
   
3. $\angle A={45}^{\circ }$
   
4. $\angle A={30}^{\circ }$
   

Q.

If AD is an altitude of an isosceles triangle ABC in which AB = AC. Then:

1. BD = CD
2. BD < CD
3. None of these
4. BD > CD

Q.

The value of $x^{\circ }$ in the given figure is _______

1. ${60}^{\circ }$
   

2. ${30}^{\circ }$
   

3. ${15}^{\circ }$

4. ${45}^{\circ }$
   

Q. In a right isosceles triangle PQR right angled at Q, what are the angles of P and R?

1. ${45}^{\circ },{45}^{\circ }$
2. ${45}^{\circ },{55}^{\circ }$
3. ${30}^{\circ },{60}^{\circ }$
4. ${35}^{\circ },{55}^{\circ }$

Q. In the given figure, LM = LN and $\angle PLN={110}^{\circ }$. Find $\angle LMN$.

1. 70

Q.

Question 1 (i)
In an isosceles triangle ABC, with AB = AC, the bisectors of $\angle Band\angle Cintersect$
each other at O. Join A to O. Show that:
OB = OC

Q. From the figure, which among the following is correct?

1. $\angle ADC=\angle CBE$
2. $\angle ACD=\angle CEB$
3. $\angle ACD=\angle CAD$
4. $\angle ACD=\angle CBE$

Q. If the perimeter of triangle ABC is 14 cm such that AB = AC and BC = 6 cm, then find the length of AB.

1. 3 cm
2. 5 cm
3. 6 cm
4. 4 cm

Q.

In the given figure, AB||CD and if $\angle$CFE=${90}^{\circ }$, then $\angle$FEB= ___ degree.

Q. Which of the following is correct for the figure.

1. Acute Isosceles Triangle
2. None of these
3. Obtuse Isosceles Triangle
4. Right Isosceles Triangle

Q.

The perimeter of a triangle is $1.72m$. If its two sides measure $0.81m$ and $0.46m,$ find the measure of its third side in $cm.$

Q. ABC is an isosceles triangle such that AB = AC in which altitude AD is drawn. Which among the following is correct?

1. AD is also a perpendicular bisector of BC.
2. AD is also a median.
3. $\angle BAD=\angle CAD$
4. All of these

Q. Question 20
Prove that in a triangle, other than an equilateral triangle, angle opposite the longest side is greater than $\frac{2}{3}$ of a right angle.

Q.

In a right triangle, prove that the square of the hypotenuse is equal to the sum of squares of the other two sides.

Using the above, solve the following:

From figure, find the length of $CAifCD\perp DBandAB\perp DB$

Q. In the given figure, LM = LN and $\angle PLN={110}^{\circ }$. Find $\angle LMN$.

1. $\angle LMN={70}^{\circ }$
2. $\angle LMN={60}^{\circ }$
3. $\angle LMN={50}^{\circ }$
4. $\angle LMN={40}^{\circ }$

Q.

Can you make a $trianglewith5matchstick$?

Q. If $\Delta ABC$ is a triangle such that AB = BC and $\angle B={120}^{\circ }$, then what are the other pair of angles?

1. ${30}^{\circ },{30}^{\circ }$
2. ${60}^{\circ },{30}^{\circ }$
3. ${45}^{\circ },{30}^{\circ }$
4. ${50}^{\circ },{30}^{\circ }$

Q. Which among the following pair of angles represent isosceles triangle?

1. ${60}^{\circ },{30}^{\circ },{90}^{\circ }$
2. ${30}^{\circ },{30}^{\circ },{120}^{\circ }$
3. ${60}^{\circ },{40}^{\circ },{80}^{\circ }$
4. ${45}^{\circ },{55}^{\circ },{80}^{\circ }$

Q. Draw the triangles as suggested.
(a) An acute angled isosceles triangle.
(b) An obtuse angled scalene triangle
(c) A right angled isosceles triangle.
(d) An acute angled scalene triangle.
(e) An obtuse angled isosceles triangle.

Q. An isosceles triangle ABC has AC = BC. CD bisects AB at D and $\angle$ CAB = 55^o. Find $\angle ACB$.

1. 70

Q.

One of the set squares from Andy's geometry box had two equal side lengths. The triangle which is similar to that set square with two equal sides is__ triangle.​

Q. In triangleABC, if M is circumcentre, AC=BC and angleAMB=130, then the measure of angleCAB equal

Q.

Two sides $PQ$ and $QR$ of $∆PQR$ are $28cm$ and $38cm$ respectively. Find the length of its third side $PR$ if perimeter of $∆PQR$ is $100cm$​