Two angles are said to be complementary angles if their sum is 90 degrees. The angles A and B shown in the figure are complementary since their angle sum is 90°. + B = 90° B Two angles are said to be supplementary angles if their sum is 180 degrees. The angles A and B shown in the figure are complementary since their angle sum is 180°.
The number of all possible angles is infinite and no figure can show them all.
A parallelogram does not equal 180. A parallelogram is a plane figure bounded by two pairs of parallel lines. What does equal 180 is the sum of the measures of any pair of adjacent angles. The two adjacent angles have a side in common. If that line is considered as the intercept of the pair of parallel lines, it is easy to show that the angles should add to 180 degrees.
A rhombus is a shape with one pair of parallel sides. I has four sides and angles.
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If you wan't to show that a pentagon has no right angles, then don't put any right angle signs in the figure.
Because the 4 interior angles of any quadrilateral add up to 360 degrees and a cyclic quadrilateral diagonals opposite angles add up to 180 degrees therefore it follows that the other pair must be 180 degrees
To prove that a quadrilateral is a right trapezoid, you need to show that it has one pair of parallel sides and one pair of right angles. This can be done by using the properties of parallel lines and perpendicular lines.
A pair of parallel lines with a transversal will have the following pairs of angles. Alternate , Corresponding, Allied internal, allied external and Vertically Opposite. Unfortunately I cannot draw a diagram on this site in order to show you the positions of these angle - pairs.
Cannot show a picture, but visualise a right angled triangle. Then imagine one of the [acute] vertices chopped off by a line parallel to the opposite side. You will then have a trapezium with two right angles. Very crudely, it should look like the figure below: ---\ |__\
Nothing else, the angle-angle-side is sufficient to show the triangles are congruent. With two corresponding angles are equal, the third angles in the triangles by definition (the sum of the three angles in a triangle is 180o) must be equal making the triangles similar. If a corresponding pair of sides are also equal, then the other two corresponding pairs of sides will be equal.
You show that they have the same measure.
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.