If the diagonals of a parallelogram are equal then show that it is a rectangle

They are just ways to identify similar or congruent triangles. The S stands for corresponding sides of equal measure on each triangle, and the A stands for corresponding angles of equal measure on each triangle. So for SSS, all three sides of a triangle would have the same lengths of all of the sides of another triangle. For AAA (or just AA, because you only need two of the angles) it would be the same thing, all three angles of a triangle would be the same as the angles on another triangle. However, because no sides must be related in this case, you are only getting similar triangles, not congruent ones. For ASA and SAS, two angles (ASA) or two sides (SAS) and the angle (for SAS) or a side (for ASA) that is surrounded by the two sides/angles; if these measures are equal to measures in the same position of another triangle, then they are congruent (an example of ASA would be at 2:30). ASS and SSA don't actually work, but AAS and SAA work. For those comparisons, if two angles and a side that is not between them have the same measure as another triangle's two angles and an outside side, then both of those are congruent. It is really difficult to explain it without having any visuals, but I would have thought that the KA videos would have explained it well enough, but I haven't seen them, so I don't know. Lets talk about a square. If it is a square, then it is a quadrilateral with all right angles and congruent sides. If a quadrilateral has all right angles and congruent side...

Hint – To prove it is a rectangle, we draw its diagonals and then compare the triangles formed w.r.t the diagonals. We use properties of triangles to find the angles of the figure. Complete step-by-step answer: Given Data, in parallelogram ABCD, AC = BD. To prove: Parallelogram ABCD is rectangle. Proof: Let us consider ∆ACB and ∆BDA from the figure Let us compare their sides, AC = BD (given) They have a common side, i.e. AB = BA We know the opposite sides of a parallelogram are equal, hence BC = AD The SSS rule states that: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. ⟹$\Delta ^\circ $ Hence the angles in the figure are 90°, i.e. the given parallelogram is a rectangle. Note – In order to solve this type of problem the key is to use the given data in the question and draw an appropriate figure. Upon drawing the figure we use the properties of diagonals and triangles formed to prove that the angles inside the figure are 90°, to prove it as a rectangle. In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points.

Given : | | gm ABCD in which A C = B D To Prove : ABCD is rectangle. Proof : In Δ A B C a n d Δ A B D A B = A B (Common) A C = B D (Given) B C = A D (opposite sides of | | g m ) ∴ Δ A B C ≅ Δ A B D (S.S.S. Rule) ∴ ∠ A = ∠ B B u t A D | | B C ( ∴ opp. sides of | | g m a r e | | ) ∴ ∠ A + ∠ B = 180 ∘ ∴ ∠ A = ∠ B = 90 ∘ Similarly ∠ D = ∠ C = 90 ∘ Hence ABCD is a rectangle. .