Properties of Isosceles Triangle

Q.

In a $\Delta ABC,ifAB=ACand\angle B={70}^{\circ },find\angle A.$

Q.

In triangles ABC and PQR, AB = AC, $\angle$C = $\angle$P and $\angle$B = $\angle$Q. The two triangles are ___.

1. isosceles and congruent

2. congruent but not isosceles

3. neither congruent nor isosceles

4. isosceles but not congruent

Q.

$In\Delta ABC,\angle C=\angle A,\text{BC = 4 cm and AC = 5 cm. Then, AB =?}\text{(a) 4 cm (b) 5 cm (c) 8 cm (d) 2.5 cm}$

Q. Question 6
ABC is a right triangle with AB = AC. If bisector of $\angle A$ meets BC at D, then prove that BC = 2AD.

Q.

ABC is an isosceles triangle such that AB = AC and AD is the median to base BC, then, $\angle BAD=$

1. ${70}^{\circ }$

2. ${55}^{\circ }$

3. ${35}^{\circ }$

4. ${110}^{\circ }$

Q.

In the figuere, if $AE||DCandAB=AC,\text{the value of}\angle ABDis$

1. ${110}^{\circ }$

2. ${120}^{\circ }$

3. ${130}^{\circ }$

4. ${70}^{\circ }$

Q.

ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.

Q.

Angles A, B, C of a triangle ABC are equal to each other. Prove that $\Delta ABC$ is equilateral.

Q.

ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.

Q.

In the figure, ABC is isosceles triangle whose side AC is produced E. Through C, CD is drawn parallel to BA. The value of x is

1. ${104}^{\circ }$

2. ${52}^{\circ }$

3. ${76}^{\circ }$

4. ${156}^{\circ }$

Q.

$△\mathrm{ABC}$ is an isosceles triangle with $\mathrm{AB}=\mathrm{AC}$ and $\mathrm{BD}$ and $\mathrm{CE}$ are its two medians. Show that$\mathrm{BD}=\mathrm{CE}$.

Q.

In a $\Delta ABC,ifAB=AC\text{and BC is produced}$

$\text{to D such that}\angle ACD={100}^{\circ },then\angle A=$

1. ${20}^{\circ }$

2. ${40}^{\circ }$

3. ${60}^{\circ }$

4. ${80}^{\circ }$

Q.

The radius of two similar right circular cylinders are 4 cm and 6cm. The ratio of their altitudes is

1. 4 : 9

2. 2 : 9

3. 4 : 3

4. 2 : 3

Q.

Prove that the medians corresponding to equal sides of an isosceles triangle are equal.

Q.

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is

1. ${100}^{\circ }$

2. ${120}^{\circ }$

3. ${110}^{\circ }$

4. ${130}^{\circ }$

Q.

The vertical angle of an isosceles triangle is ${100}^{\circ }.$ Find its base angles.

Q.

In a $\Delta ABC,if\angle A={120}^{\circ }andAB=AC.Find\angle Band\angle C.$

Q.

In the given figure, O is the centre of a circle. Then $\angle OAB=?$

(a) ${50}^{\circ }$

(b) ${60}^{\circ }$

(c) ${55}^{\circ }$

(d) ${65}^{\circ }$

Q.

$In\Delta ABC,\text{AB = AC and}\angle B={50}^{\circ }.Then\angle A=?\left(a\right){40}^{\circ }\left(b\right){50}^{\circ }\left(c\right){80}^{\circ }\left(d\right){130}^{\circ }$

Q.

The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the corresponding sides containing the angle.Prove it.

Q.

In fig. TQ and TR are bisectors of $\angle$Q and $\angle$R respectively. If $\angle$QPR = ${80}^{\circ }$ and $\angle$PRT = ${30}^{\circ }$. Determine $\angle$TQR. [4 MARKS]

Q.

In the figure, AB = AC and $\angle ACD={105}^{\circ },find\angle BAC.$

Q.

In the given figure, $△$ABC is an isosceles triangle in which AB =
AC and a circle passing through B and C intersects AB and AC at D and E respectively.

Prove that DE||BC.

Q. Question 1
In figure, if $AB||CD||EF,PQ||RS,\angle RQD={25}^{\circ }and\angle CQP={60}^{\circ },then\angle QRS$ is equal to:


A) ${85}^{\circ }$
B) ${135}^{\circ }$
C) ${145}^{\circ }$
D) ${110}^{\circ }$

Q. In triangle ABC, if AB = AC, then angle B = 45 degree, then find angle C.

1. 75 degree
2. 65 degree
3. 45 degree
4. 30 degree

Q. Question 4
In $\Delta ABC$, if BC =AB and $\angle B={80}^{\circ }$ then $\angle A$ is equal to
(A) ${80}^{\circ }$
(B) ${40}^{\circ }$
(C) ${50}^{\circ }$
(D) ${100}^{\circ }$

Q.

Through any point in the bisector of an angle, a straight line is drawn parallel to either arm of the angle. Prove that the triangle so formed is isosceles.

Q.

P is a point on the bisector of an angle $\angle ABC.$ If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.

Q. 6. three altitudes of a triangle are 10cm 12cm and 15cm , find semiperimeter of triangle

Q.

Which is the triangle in which two of the altitudes are same as the sides?

1. Isosceles Triangle
2. Right Triangle
3. Equilateral Triangle
4. Scalene Triangle