Question

directions: complete the following questions by showing all work and annotations. keep work organized and box any final answer. all work must be shown in order to receive full credit. **#1.) which of the following is true only when a parallelogram is a rhombus? a. all angles are right angles b. diagonals bisect each other c. diagonals are congruent d. all sides are congruent explain: #2.) when is a rectangle a square? a) when diagonals are congruent b) when diagonals bisect each other c) when diagonals bisect angles d) when all four angles are right angles explain:

Explanation:

Question 1

To solve this, we recall the properties of parallelograms and rhombuses:

• A parallelogram has opposite sides parallel and equal, diagonals bisect each other.
• A rhombus is a parallelogram with all sides equal.
• Option a: All angles right angles is a rectangle (a type of parallelogram), not unique to rhombus.
• Option b: Diagonals bisect each other is true for all parallelograms, not just rhombuses.
• Option c: Diagonals congruent is true for rectangles (a type of parallelogram), not rhombuses (unless it's a square, but not unique to rhombus).
• Option d: All sides congruent is the defining property of a rhombus among parallelograms (since other parallelograms have opposite sides equal, but not all four sides equal unless it's a rhombus).

Recall properties of rectangles and squares:

• A rectangle has four right angles and opposite sides equal.
• A square is a rectangle with all sides equal (and four right angles).
• Option a: Diagonals congruent is true for all rectangles, not unique to squares.
• Option b: Diagonals bisect each other is true for all rectangles (since they are parallelograms), not unique to squares.
• Option c: Diagonals bisect angles is a property of a square (and rhombus). In a rectangle (that's not a square), diagonals don't bisect the angles (since adjacent sides are unequal, the angles formed by diagonals are not equal). So when a rectangle's diagonals bisect the angles, it means all sides are equal (so it's a square).
• Option d: All four angles right angles is true for all rectangles, not unique to squares.

Answer:

d. All sides are congruent

Question 2