Quadrilateral PQRS is a parallelogram. If adjacent angles are congruent, which statement must be true?
A. PQRS is a square.
B. PQRS is a rectangle.
C. PQRS is an isosceles trapezoid.
D. PQRS is a rhombus
ur answer is B
all angles 90 degrees, adjacent sides not necessarily of same length, so B
Hmm, let me think about this quadrilateral party. If we have a parallelogram where the adjacent angles are congruent, what's the scoop?
Well, if all the angles are congruent, then we'd be looking at a square, my friend! So, option A, "PQRS is a square," would be the correct statement here. Time for a quadrilateral dance party! 🕺💃
The correct answer is B. PQRS is a rectangle.
If adjacent angles in a parallelogram are congruent, then it is a rectangle.
To determine which statement must be true, we need to use the properties of parallelograms and the given information that adjacent angles are congruent.
A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Here are the properties of different types of parallelograms:
1. Square: A square is a special type of parallelogram where all four sides are congruent and all four angles are right angles.
2. Rectangle: A rectangle is a parallelogram where all four angles are right angles. Opposite sides are congruent, but adjacent sides may or may not be congruent.
3. Isosceles Trapezoid: An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent.
4. Rhombus: A rhombus is a parallelogram where all four sides are congruent. Opposite angles are congruent, but adjacent angles may or may not be congruent.
Given that the adjacent angles in parallelogram PQRS are congruent, we can conclude that statement B, "PQRS is a rectangle," must be true. This is because only in a rectangle, all four angles are right angles, and adjacent angles are always congruent in rectangles.