0
What else can I help you with?
The sum of interior angles of a square is?
360 degrees. Same for any other rectangle, rhombus, parallelogram, or convex quadrilateral. The reason is that any quadrilateral can be divided into two triangles by drawing a diagonal and the sum of the angles of each triangle is 180 degrees.
If one pair of opposite angles and one pair of opposite sites of a quadrilateral is congruent then the quadrilateral is a parallelogram. How can it be proven?
draw a diagonal through opposite corners of the quadrilateral. This makes two triangles. Prove the triangles are congruent using SSA (side side angle) congruence. Then show that the other two sides of the quadrilater must be congruent to each other, so it is a parallelogram.
How do you find the sum of the measures of the angles of a quadrilateral?
I'm not sure if you mean interior or exterior angles, so I'll give you an answer for both.For interior angles:The sum of the measures of the *interior* angles of a quadrilateral is always 360 degrees. To understand why this is true, recall that the sum of the interior angles of a triangle is 180 degrees. Now, in any quadrilateral, we can draw a diagonal, splitting it into two triangles.So, the sum of the interior angles of the quadrilateral will be the sum of all of the interior angles of the two triangles, in other words, 2x180.In general, an n-gon can be divided into n-2 triangles, so the sum of the interior angles of an n-gon is 180x(n - 2) = 180xn - 360For exterior angles:The sum of the exterior angles of any closed, convex figure will be 360 degrees. So, if the quadrilateral is convex (isn't bent inwards) the sum of the exterior angles will be 360 as well.
What geometric shapes have acute angles?
Any irregular polygon can have an acute angle. A regular triangle (equilateral) has three acute angles. All other triangles must have at least two acute angles. A quadrilateral, other than a rectangle (or square), must have at least one.
How is a quadrilateral different from a quadrilateral?
A rhombus is a 4 equal sided quadrilateral with equal opposite acute angles and equal opposite obtuse angles with diagonals that bisect each other at right angles.
Why all quadrangle sum to 360 degree?
It can be proven that the angle sum of a triangle is 180 degrees using Euclid's parallel postulate. Any quadrilateral can be divided into two triangles by connecting two opposite sides. The sum of the angles of the quadrilateral will be the sum of the sum of the two triangles, or in other words 2*180=360. In fact, any n-gon can be divided into n-2 triangles and the sum of the angles of the n-gon will be (n-2)*180.
What is a quadrilateral with the diagonals forming right angles?
If the diagonals of a quadrilateral are perpendicular to each other, then the quadrilateral is a square.Or a kite.
What angles are equal in similar triangles?
If the triangles are similar, then each of the three angles in one of them is equal to the corresponding angle in the other one.
Why do you think that diagonals bisect each other for proving that a quadrilateral is a parallelogram?
The diagonals divide the quadrilateral into four sections. You can then use the bisection to prove that opposite triangles are congruent (SAS). That can then enable you to show that the alternate angles at the ends of the diagonal are equal and that shows one pair of sides is parallel. Repeat the process with the other pair of triangles to show that the second pair of sides is parallel. A quadrilateral with two pairs of parallel lines is a parallelogram.
One quadrilateral that has no right angles and no parallel sides is a?
It's a quadrilateral. There's no other name for it.
Do similar triangles always have congruent angles?
Yes, in similar triangles, the angles are always congruent, and the sides have the same proportions to each other.
Is it possible to have a quadrilateral with 2 reflex angles?
No. All quadrilaterals can be made from joining two triangles, hence they all have interior angles that sum to 360 degrees. Reflex angles are greater than 180 degrees so two reflex angles would be too big!
