Basic Concepts in Geometry Maths - Basic Concepts in Geometry

If P – Q – R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).

Find d(A, B), if co-ordinates of A and B are – 2 and 5 respectively.

How many lines are determined by three distinct points?

How many points are there in the intersection of two distinct lines ?

How many midpoints does a segment have ?

Given below are four points P, Q, R, and S. Check which three of them are collinear and which three are non collinear. In the case of three collinear points, state which of them is between the other two.

Points A, B, C are given below. Check, with a stretched thread, whether the three points are collinear or not. If they are collinear, write which one of them is between the other two.

Write the converse of each of the following statements : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.

Write the converse of each of the following statements : If the corresponding angles formed by a transversal of two lines are congruent, then the two lines are parallel.

Write the converse of each of the following statements : If the sum of measures of two angles is 90°, thfcn they are eomplement of each other.

How had you verified that light rays travel in a straight line? Recall an experiment in science which you have done in a previous standard.

Students are asked to stand in a line for mass drill. How will you check whether the students standing are in a line or not ?

Write the antecedent (given part) and the consequent (part to be proved) in the following statements : The diagonals of a parallelogram bisect each other.

Write the antecedent (given part) and the consequent (part to be proved) in the following statements : If all sides of a triangle are congruent, then its all angles are congruent.

The co-ordinate of point A on a number line is 5. Find the co-ordinates of points on the same number line which are 13 units away from A.

Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent : If the altitudes drawn on two sides of a triangle are congruent, then these two sides are congruent.

Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent : If angles in a linear pair are congruent, then each of them is a right angle.

Draw a labelled figure showing information in each of the following statements and write the antecedent and the consequent : Two equilateral triangles are similar.

Write converses of the following statements.
i. The alternate angles formed by two parallel lines and their transversal are congruent.
ii. If a pair of the interior angles made by a transversal of two lines are supplementary, then the lines are parallel.
iii. The diagonals of a rectangle are congruent.

Write the following statements in ‘if-then’ form.
i. The opposite angles of a parallelogram are congruent.
ii. The diagonals of a rectangle are congruent.
iii. In an isosceles triangle, the segment joining the vertex and the midpoint of the base is perpendicular to the base.

Co-ordinate of point A on a number line is 1. What are the co-ordinates of points on the number line which are at a distance of 7 units from A ?

Co-ordinate of point P on a number line is – 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.

Sketch proper figure and write the answers of the following questions. [2 Marks each]
i. If A – B – C and l(AC) = 11,
l(BC) = 6.5, then l(AB) = ?
ii. If R – S – T and l(ST) = 3.7,
l(RS) = 2.5, then l(RT) = ?
iii. If X – Y – Z and l(XZ) = 3√7,
l(XY) = √7, then l(YZ) = ?

Points X, Y, Z are collinear such that d(X, Y) = 17, d(Y, Z) = 8, find d(X, Z).

On a number line, points A, B and C are such that d(A, C) = 10, d(C, B) = 8. Find d(A, B) considering all possibilities.

On a number line, co-ordinates of P, Q, R are 3,-5 and 6 respectively. State with reason whether the following statements are true or false.
i. d(p, Q) + d(Q, R) = d(P, R)
ii. d(P, R) + d(R, Q) = d(P, Q)
iii. d(R, P) + d(P, Q) = d(R, Q)
iv. d(P, Q) – d(P, R) = d(Q, R)

Answer the questions with the help of figure given below
.
i. State the points which are equidistant from point B.
ii. Write a pair of points equidistant from point iii. Find d(U,V), d(P,C), d(V,B), d(U, L).

Write the answers to the following questions with reference to the figure given below:

i. Write the name of the opposite ray of ray RP
ii. Write the intersection set of ray PQ and ray RP.
iii. Write the union set of ray PQ and ray QR.
iv. State the rays of which seg QR is a subset.
v. Write the pair of opposite rays with common end point R.
vi. Write any two rays with common end point S.
vii. Write the intersection set of ray SP and ray ST.

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.

i. seg DE and seg AB
ii. seg BC and seg AD
iii. seg BE and seg AD

If the co-ordinate of A is x and that of B is . y, find d(A, B).
i. x = 1, y = 7
ii. x = 6, y = -2
iii. x = -3, y = 7
iv. x = -4, y = -5
v. x = -3, y = -6
vi. x = 4, y = -8