Question

given the information marked on each figure below, select all classifications that must be true. note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determin if necessary, you may learn what the markings on a figure indicate. for the first figure (g, h, i, j): - quadrilateral (checkbox) - parallelogram (checkbox) - rectangle (checkbox) for the second figure (a, b, c, d): - quadrilateral (checkbox) - parallelogram (checkbox) - rectangle (checkbox) for the third figure (k, l, m, n): - quadrilateral (checkbox) - parallelogram (checkbox) - rectangle (checkbox)

Explanation:

First Figure (G, H, I, J):

• Quadrilateral: It has 4 sides, so it's a quadrilateral.
• Parallelogram: If all angles are right angles (marked as such), opposite sides are parallel and equal, so it's a parallelogram.
• Rectangle: A quadrilateral with four right angles is a rectangle.

Second Figure (A, B, C, D):

• Quadrilateral: 4 - sided figure, so quadrilateral.
• Parallelogram: Opposite sides are marked equal (tick marks) and one angle is a right angle, so opposite sides are parallel and equal, making it a parallelogram.
• Rectangle: A parallelogram with a right angle is a rectangle (since in a parallelogram, if one angle is right, all are right).

Third Figure (K, L, M, N):

• Quadrilateral: 4 - sided, so quadrilateral.
• Parallelogram: If opposite angles are equal (marked with same angle marks) and consecutive angles are supplementary (implied by right - angle - like and other angle marks), opposite sides are parallel, so it's a parallelogram.
• Rectangle: If we can infer that all angles are right angles (from the angle markings, since in a parallelogram with opposite angles equal and some right - angle - like marks, all angles are right), then it's a rectangle.

Answer:

• First Figure (G, H, I, J): Quadrilateral, Parallelogram, Rectangle (all three options are true).
• Second Figure (A, B, C, D): Quadrilateral, Parallelogram, Rectangle (all three options are true).
• Third Figure (K, L, M, N): Quadrilateral, Parallelogram, Rectangle (all three options are true).