Special Points in a Triangle

Q.

Construct a triangle ABC, with AB=7 cm, BC= 8 cm and $\angle ABC={60}^o$. Locate by construction the point P such that:

(i) P is equidistant from B and C.

(ii) P is equidistant from AB and BC.

Measure and record the length of PB.

Q. Construct a triangle similar to a given ΔXYZ with its sides equal to (3/4)^th of the corresponding sides of ΔXYZ. Write the steps of construction.

Q.

Construct a right angled triangle PQR, in which $\angle Q={90}^o$, hypotenuse PR=8 cm and QR=4.5 cm. Draw bisector of angle PQR and let it meet PR at point T. Prove that T is equidistant from PQ and QR.

Q.

Construct a triangle ABC in which BC is 8 cm, Angle B is ${75}^{\circ }$and AB+AC=15cm by using the method of perpendicular bisector.by using the method of perpendicular bisector.

Q.

Construct a triangle ABC, with AB= 6 cm, AC=BC=9 cm.Find a point 4 cm from A and equidistant from B and C.

Q.

Construct a triangle BCP given BC= 5 cm, BP= 4 cm and $\angle PBC={45}^o$.

(i) Complete the rectangle ABCD such that:

(a) P is equidistant from AB and BC.

(b) P is equidistant from C and D.

(ii) Measure and record the length of AB.

Q.

Construct an isosceles triangle with base 6cm and height 7cm. Construct another triangle similar to this, with ratio of corresponding sides as 4:3.

Q.

Use graph paper for this question.Take 2 cm = 1 unit on both the axes.

(i) Plot the points A(1, 1) , B(5, 3) and C(2, 7).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Locate the point P such that PA=PB and P is equidistant from AB and AC.

(v) Measure and record the length PA in cm.

Q.

Draw a right triangle in which the sides (other than hypotenuse) are of lengths $4\mathrm{cm}\mathrm{and}3\mathrm{cm}$. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle. Give the justification for the construction

Q.

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

Q. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are (2/3) of the corresponding sides of it.

Q.

The point which lies on the perpendicular bisector of line segment joining the points A(-2, -5) and B(2, 5)is

a) (0, 0) b) (0, 2) c) (2, 0) d) (-2, 0)

Q. Match the following with name of the point of intersection of the lines given in figure.

1. Centroid
2. Incentre
3. Orthocentre

Q. where does the perpendicular bisector of line segment joiningthe points A(1, 5)and B(4, 6) cut the y-axis?

Q.

Construct a triangle ABC, with AB=5.6 cm, AC=BC=9.2 cm.

Find the points equidistant from AB and AC; and also 2 cm from BC.

Measure the distance between the two points obtained.

Q.

Construct a triangle ABC, in which $ABC={75}^o$, AB=5 cm and BC=6.4 cm. Draw perpendicular bisector of side BC and also the bisector of Angle ACB.If these bisectors intersect each other at point P;prove that P is equidistant from B and C; and also from AC and BC.

Q. Construct a ∆ABC in which AB = 5 cm, BC = 6 cm and CA = 7 cm. Construct a triangle similar to ∆ABC, such that each of its side is $\frac{5}{7}$ the corresponding sides of ∆ABC.

Q.

Construct a triangle ABC, having given AB= 4.8 cm, AC=4 cm, and $\angle A={75}^o$.Find a point P

(i) inside the triangle ABC;

(ii) outside the triangle ABC;

equidistant from B and C; and at a distance of 1.2 cm from BC.

Q. Match the following with their point of intersection

1. Side bisector
2. Angle bisector
3. Altitude
4. Medians

Q. Construct $∆$LMN, such that LM = 6.2 cm, MN = 4.9 cm, LN = 5.6 cm.

Q. Construct $∆$LEM, such that, LE = 6 cm, LM = 7.5 cm, $\angle$LEM = 90$°$ and draw its circumcircle.

Q.

What is the difference between the application of mid-point formulae and section formulae

Q. Construct the incircle of $∆$DEF in which DE = EF= 5.8 cm, $\angle$DEF= 65$°$ .

Q. Construct a ∆ABC in which AB = 5 cm, BC = 6 cm and CA = 7 cm. Construct a triangle similar to ∆ABC, such that each of its side is the corresponding sides of ∆ABC.

Q. The centroid divides the length of median in the ratio of 2:1.

1. True
2. False

Q.

Describe the locus for questions 1 to 13 given below:

The locus of vertices of all isosceles triangles having a common base.

Q.

Construct a triangle with sides $5cm,6cm$ and $7cm$ and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Q. The line joining the centroid and the vertices of a triangle divides the triangle in three equal area.

1. No
2. Yes