Question

quadrilateral m has 4 congruent sides. quadrilateral l has 2 pairs of parallel sides and congruent diagonals. quadrilateral t has at least 1 pair of parallel sides that are also congruent. quadrilateral x has exactly 1 pair of parallel sides that are not congruent. the other pair of sides are congruent. select all of the statements that must be true based on the given information. base angles of quadrilateral t are congruent. base angles of quadrilateral x are congruent. opposite angles of quadrilateral m are congruent. opposite angles of quadrilateral l are congruent. consecutive angles of quadrilateral x are congruent. consecutive angles of quadrilateral l are congruent. opposite angles of quadrilateral m are supplementary.

Explanation:

Step1: Identificar las figuras

• Quadrilateral M: es un rombo (4 lados congruentes).
• Quadrilateral L: es un rectángulo (2 pares de lados paralelos y diagonales congruentes).
• Quadrilateral T: es un paralelogramo (al menos 1 par de lados paralelos y congruentes).
• Quadrilateral X: es un trapecio isósceles (exactamente 1 par de lados paralelos no congruentes y el otro par de lados congruentes).

Step2: Analizar las propiedades de cada figura

• Base angles of Quadrilateral T: En un paralelogramo, los ángulos opuestos son congruentes, no los ángulos de base.
• Base angles of Quadrilateral X: En un trapecio isósceles, los ángulos de base son congruentes.
• Opposite angles of Quadrilateral M: En un rombo, los ángulos opuestos son congruentes.
• Opposite angles of Quadrilateral L: En un rectángulo, los ángulos opuestos son congruentes (todos son \(90^{\circ}\)).
• Consecutive angles of Quadrilateral X: En un trapecio isósceles, los ángulos consecutivos no son necesariamente congruentes.
• Consecutive angles of Quadrilateral L: En un rectángulo, los ángulos consecutivos son congruentes (todos son \(90^{\circ}\)).
• Opposite angles of Quadrilateral M: En un rombo, los ángulos opuestos no son necesariamente suplementarios (a menos que sea un cuadrado).

Answer:

• Base angles of Quadrilateral X are congruent.
• Opposite angles of Quadrilateral M are congruent.
• Opposite angles of Quadrilateral L are congruent.