ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).
Uploaded bysandeep View Answer
Explain why a rectangle is a convex quadrilateral.
Name the quadrilaterals whose diagonals.
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal
Explain how a square is.
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle
Identify all the quadrilaterals that have
(a) four sides of equal length
(b) four right angles
State whether True or False.
(a) All rectangles are squares.
(b) All rhombuses are parallelograms.
(c) All squares are rhombuses and also rectangles.
(d) All squares are not parallelograms.
(e) All kites are rhombuses.
(f) All rhombuses are kites.
(g) All parallelograms are trapeziums.
(h) All squares are trapeziums.
Find the measure of ∠P and ∠S, if in the following figure. (If you find m∠R, is there more than one method to find m∠P?)
Find m∠C in the following figure if
Explain how this figure is a trapezium. Which of its two sides are parallel?
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)
(i)
(ii)
The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
Can a quadrilateral ABCD be a parallelogram if
(i) ∠ D + ∠ B = 180°?
(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?
(iii) ∠ A = 70° and ∠ C = 65°?
Consider the following parallelograms. Find the values of the unknowns x, y, z.
(iii)
(iv)
(v)
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = ...
(ii) ∠ DCB = ...
(iii) OC = ...
(iv) m∠ DAB + m∠ CDA = ...
(a) What is the minimum interior angle possible for a regular polygon?
(b) What is the maximum exterior angle possible for a regular polygon?
(a) Is it possible to have a regular polygon with measure of each exterior angle as 22°?
(b) Can it be an interior angle of a regular polygon? Why?
How many sides does a regular polygon have if each of its interior angles is 165°?
How many sides does a regular polygon have if the measure of an exterior angle is 24°?
Find the measure of each exterior angle of a regular polygon of
(i) 9 sides
(ii) 15 sides
Find x in the following figures.
(a)
(b)
(a) find x + y + z
(b) find x + y + z + w
Find the angle measure x in the following figures.
(c)
(d)
What is a regular polygon?
State the name of a regular polygon of
(i) 3 sides
(ii) 4 sides
(iii) 6 sides
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)
Figure
Side
3
4
5
6
Angle sum
180°
2 × 180°
= (4 - 2) × 180°
3 × 180°
= (5 - 2) × 180°
4 × 180°
= (6 - 2) × 180°
What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
How many diagonals does each of the following have?
(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle
Given here are some figures.
(1)
(2)
(3)
(4)
(5)
(6)
sandeep View Answer