M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 11 mid point theorem

Exercises in Chapter 11 mid point theorem Grade 9

Mid Point Theorem Exercise 11

Questions in Mid Point Theorem Exercise 11

(a) In the figure (1) given below, D, E, and F are mid-points of the sides BC, CA, and AB respectively of Δ

ABC. If AB = 6 cm, BC = 4.8 cm and CA = 5.6 cm, find the perimeter of (i) the trapezium FBCE (ii) the

triangle DEF.

(b) In figure (2) given below, D and E are mid-points of the sides AB and AC respectively. If

BC = 5.6 cm and ∠B = $72^{0}$

compute (i) DE (ii) ∠ADE.

DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.

Prove that the four triangles formed by joining in pairs the mid-points of the sides C of a triangle are

congruent to each other

If D, E and F are mid-points of sides AB, BC and CA respectively of an isosceles triangle ABC, prove

that Δ DEF is also isosceles.

. The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the midpoint of AD, prove

that

(i) PQ || AB

(ii) PO = ½ CD

In the adjoining figure, ABCD is a quadrilateral in which P, Q, R and S are mid-points of AB, BC, CD

and DA respectively. AC is its diagonal. Show that

(i) SR || AC and SR = ½ AC

(ii) PQ = SR

(iii) PQRS is a parallelogram.

Show that the quadrilateral formed by joining the mid-points of the adjacent sides of a square, is also a

square.

In the adjoining figure, AD and BE are medians of Δ ABC. If DF || BE, prove that CF = ¼ AC.

In the figure (1) given below, ABCD is a parallelogram. E and F are mid-points of the sides AB and CO

respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H

respectively. Prove that

(i) Δ HEB = Δ HCF

(ii) GEHF is a parallelogram

ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC

respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.

(a) In the quadrilateral (1) given below, AB || DC, E and F are the mid-points of AD and BD

respectively. Prove that:

(i) G is the mid-point of BC

(ii) EG = ½ (AB + DC)

(b) In the quadrilateral (2) given below, AB || DC || EG. If E is mid-point of AD prove that:

(i) G is the mid-point of BC

(ii) 2EG = AB + CD

E and F are mid-point of non-parallel sides AD and BC respectively. Calculate:

(i) EF if AB = 6 cm and DC = 4 cm.

(ii) AB if DC = 8 cm and EF = 9 cm.

(a) In the quadrilateral (1) given below, AD = BC, P, Q, R, and S are mid-points of AB, BD, CD, and AC

respectively. Prove that PQRS is a rhombus.

(b) In the figure (2) given below, ABCD is a kite in which BC = CD, AB = AD, E, F, G are mid-points of

CD, BC, and AB respectively. Prove that:

(i) ∠EFG = $90^{\circ}$

(ii) The line drawn through G and parallel to FE bisects DA.

In the adjoining figure, the lines l, m, and n are parallel to each other, and G is the mid-point of CD.

Calculate:

(i) BG if AD = 6 cm

(ii) CF if GE = 2.3 cm

(iii) AB if BC = 2.4 cm

(iv) ED if FD = 4.4 cm

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Chapters in this book

Rational and Irrational Numbers

Compound Interest

Expansions

Factorization

Simultaneous Linear Equations

Problems on Simultaneous Linear Equations

Quadratic Equations

Indices

Logarithms

Triangles

Mid Point Theorem

Pythagoras Theorem

Rectilinear Figures

Theorems on Area

Circle

Mensuration

Trigonometric Ratios

Trigonometric Ratios and Standard Angles

Coordinate Geometry

Statistics