Triangle Inequality

Q.

Please explain me playfair's axiom.......and postulate 5 of Euclid proposed by him

Q.

In which of the following cases construction of a triangle is possible?

1. 10 cm, 7 cm, 3 cm

2. 10 cm, 7 cm, 6 cm

3. 9 cm, 4 cm, 7 cm

4. 9 cm, 4 cm, 5 cm

Q. For an ___ triangle, the altitude and median are the same.

Q.

In the adjoining figure, ABCD is a quadrilateral and AC is one of its diagonals. Prove that

(i) AB + BC + CD + DA > 2AC

(ii) AB + BC + CD > DA

(iii) AB + BC + CD + DA > AC + BD.

Q.

Find the breadth of a rectangular plot of land, if its area is $440m^2$ and the length is $22m$. Also find its perimeter..

Q.

. O is any point in the interior of a triangle ABC. Prove that

1. AB + AC > OB + OC

2.AB + BC + CA > OA + OB + OC

3.OA + OB + OC > 1/2(AB + AC + BC)

Q. In a quadrilateral ABCD, which of the following is true?

1. AB + BC + CD + DA < 1.5 (BD + AC)
2. AB + BC + CD + DA < (BD + AC)
3. AB + BC + CD + DA < 1.75 (BD + AC)
4. AB + BC + CD + DA < 2 (BD + AC)

Q.

Can we draw a triangle with the sides 4 cm, 7 cm and 3 cm? Give reason.

Q.

Draw a triangle and divide it into three triangles of equal area in various ways.

Q.

If O is a point within a quadrilateral ABCD, show that OA + OB + OC + OD > AC + BD

Q.

If B lies between A and C, AC = 15 cm and BC = 9 cm. What is AB?

Q.

If a, b, c are three sides of the triangle, then the perimeter of the triangle is

1. a+b+c

2. base height

3. 1/2×base×height

4. (a+b+c)/2

Q.

$AB$ and $CD$ are respectively the smallest and longest sides of a quadrilateral $ABCD$.

Show that $\angle A>\angle C$ and $\angle B>\angle D$.

Q.

Draw ΔABC, with AB = 5 cm and BC = 7 cm and ∠ABC = 60°. Draw a triangle of the same area with one side as AB and the angle at B equal to 30°

Q.

Prove that in a quadrilateral the sum of all the sides is greater than the sum of its diagonals.

Q.

In a triangle, difference of any two sides of a triangle is always less than the third side. State True/False

1. True

2. False

Q.

Two sides of a triangle are of length 4 cm and 2.5 cm. The length of the third side of the triangle cannot be

(a) 6 cm (b) 6.5 cm (c) 5.5 cm (d) 6.3 cm

Q.

Is it possible to draw a triangle with sides of length 2 cm, 3 cm and 7 cm?

Q.

Can the side lengths 3cm, 4cm, 10cm form a triangle? Say true or false

1. False

2. True

Q.

Question 6
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.

Q. Question 12
Show that in a quadrilateral ABCD, AB + BC + CD + DA > AC + BD.

Q. In the given figure, $\angle ADB=\angle ADC={90}^{\circ }.$ Also if $\angle BAD=\angle DAC$ then values of x and y are:

1. $x=15,y={100}^{\circ }$
2. $x=20,y={25}^{\circ }$
3. $x=60,y={25}^{\circ }$
4. $x=20,y={100}^{\circ }$

Q. Question 5
ABCD is a quadrilateral in which AB = BC and AD = CD. Show that BD bisects both the angles ABC and ADC.

Q. If O is a point within a quadrilateral ABCD show that OA+OB+OC+OD>AC+BD

Q.

In a triangle ABC, D is the midpoint of AB and E is a point on AC such that DE || BC. Then

1. AE=EC

2. AE= AC/2

3. Both of the above

4. Neither of the above

Q.

In a triangle ABC, AB, BC and AC are the sides, then which of the following holds true?

1. AB - BC < AC

2. AB + BC < AC

3. AB + BC = AC

4. AB - BC > AC

Q.

Prove that the sum of three altitude of a triangle is less than the sum of its sides.

Q.

In the adjoining figure, if BC = a, AC = b, AB = c and $\angle CAB$ = ${120}^{\circ }$, then the correct relation is-

1. a² = b² + c² + 2 bc

2. a² = b² + c² – 2 bc

3. a² = b² + c² + bc

4. a² = b² + c² – bc

Q. In the given figure, ABD is a triangle right angled at A and $AC\perp BD$. Then,
$A{D}^2=BD\times CD$

1. $True$
2. $False$

Q.

Construct a triangle ABC in which BC = 8 cm, ∠B = 45° and AB − AC = 3.5 cm.