Advertisements
Advertisements
प्रश्न
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!)
Advertisements
उत्तर
The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.
Here, ABCD is a convex quadrilateral, made of two triangles ΔABD and ΔBCD. Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e., 180º + 180º = 360º
Yes, this property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.
Here again, ABCD is a concave quadrilateral, made of two triangles ΔABD and ΔBCD. Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º
संबंधित प्रश्न
In a quadrilateral, define of the following Diagonals .
In the given figure, PQRS is an isosceles trapezium. Find x and y.
If ABCD is a rectangle with ∠BAC = 32°, find the measure of ∠DBC.
Use the following figure to find the value of x
The angles A, B, C and D of a trapezium ABCD are in the ratio 3: 4: 5: 6. Le. ∠A : ∠B : ∠C : ∠D = 3:4: 5 : 6. Find all the angles of the trapezium. Also, name the two sides of this trapezium which are parallel to each other. Give reason for your answer.
Observe the figure below and find out their name.
In the following figure, What is AC – EC?
What conclusion can be drawn from part of given figure, if BD bisects ∠ABC?
What conclusion can be drawn from part of given figure, if DC is the bisector of ∠ADB, CA ⊥ DA and CB ⊥ DB?
How many diagonals does a quadrilateral have?
