Best Answer

Yes. Read on for why:

Take a parallelogram ABCD with midpoints E and F in the bases. So something like this (forgive the "drawing"):

A E B

__.__

/__.__/

C F D

We know that parallelogram AEFC = EBDF, since they have the same base (F bisects CD, so CF = FD), height (haven't touched that), and angles (<ACF = <EFD because they're parallel - trust me that everything else matches).

We also know that every parallelogram can be divided into two congruent triangles along their diagonal. So if two congruent parallelograms consistent of two congruent triangles each, then all four triangles are congruent.

So your congruent triangles are ACF, AEF, EFD, and EBD.

You can further reinforce this through ASA triangle congruency proofs (as I did at first), but this is a far more concise and equally valid answer.

Q: Does a parellelogram have four congruent triangles?

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A parallelogram with equal sides is a rhombus. If the interior angles are right angles, it's a square.

You could prove two triangles are congruent by measuring each side of both triangles, and all three angles of each triangle. If the lengths of the sides are the same, and so are the angles, then the triangles are congruent... if not, then the triangles are not congruent. If the triangles have the exact same size and shape then they are congruent.

When two triangles are congruent, there are 6 facts that are true about the triangles. The triangles have 3 sets of congruent (of equal length) sides and the triangles have 3 sets of congruent (of equal measure) angles.

All the corresponding sides in congruent triangles are equal All the corresponding angles in congruent triangles are equal

No. All corresponding sides and angles have to be congruent for the triangles to be congruent.

Related questions

A tetrahedron has four equilateral triangles as sides

Parellelogram

A parallelogram with equal sides is a rhombus. If the interior angles are right angles, it's a square.

Isosceles TetrahedronA solid with four faces is a tetrahedron. Each of the faces is a triangle. If all the triangles are congruent, you have an isosceles tetrahedron.

square.......

Four.

Are congruent triangles.

An isosceles trapezoid can be subdivided into 4 right angle triangles.

sssThere are five methods for proving the congruence of triangles. In SSS, you prove that all three sides of two triangles are congruent to each other. In SAS, if two sides of the triangles and the angle between them are congruent, then the triangles are congruent. In ASA, if two angles of the triangles and the side between them are congruent, then the triangles are congruent. In AAS, if two angles and one of the non-included sides of two triangles are congruent, then the triangles are congruent. In HL, which only applies to right triangles, if the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent.

The four congruence theorem for right triangles are:- LL Congruence Theorem --> If the two legs of a right triangle is congruent to the corresponding two legs of another right triangle, then the triangles are congruent.- LA Congruence Theorem --> If a leg and an acute angle of a right triangles is congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.- HA Congruence Theorem --> If the hypotenuse and an acute angle of a right triangle is congruent to the corresponding hypotenuse and acute angle of another triangle, then the triangles are congruent.- HL Congruence Theorem --> If the hypotenuse and a leg of a right triangle is congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

If triangles have the corresponding sides congruent then they are congruent. SSS If two triangles have two sides and an included angle congruent then they are congruent. SAS If two triangles have two angles and an included side congruent then they are congruent. ASA SSA doesn't work.

You could prove two triangles are congruent by measuring each side of both triangles, and all three angles of each triangle. If the lengths of the sides are the same, and so are the angles, then the triangles are congruent... if not, then the triangles are not congruent. If the triangles have the exact same size and shape then they are congruent.