Pregunta
- If quadrilateral
is a parallelogram and
, what are the
measures of angles
, and
?
- Prove that a diagonal and the sides of a parallelogram form two congru
triangles.
measures of angles
triangles.
Ask by Lyons Harmon. in the United States
Jan 23,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
In parallelogram
:
Proof:
A diagonal in a parallelogram divides it into two congruent triangles by the Side-Angle-Side (SAS) congruence criterion.
A diagonal in a parallelogram divides it into two congruent triangles by the Side-Angle-Side (SAS) congruence criterion.
Solución

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Bonus Knowledge
In quadrilateral
, since it’s a parallelogram, opposite angles are congruent, and consecutive angles are supplementary. Given
, we can find
as follows:
. Since
and
are opposite
and
respectively,
and
.
To prove that a diagonal together with the two sides of a parallelogram forms two congruent triangles, consider diagonal
. This creates triangles
and
. Because
is common to both triangles, by the properties of parallelograms,
is parallel to
, which establishes
and
as alternate interior angles, making them congruent. Additionally,
is equal to itself, thus by the Angle-Side-Angle (ASA) postulate,
.

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