Question

a. select all quadrilaterals that you think can be decomposed into two identical triangles using only one line.

Explanation:

To solve this, we analyze each quadrilateral:

Step 1: Recall Properties of Quadrilaterals

A quadrilateral can be decomposed into two identical triangles with one line if it has a diagonal that splits it into two congruent triangles. This is true for:

• Parallelograms (including rhombuses, rectangles, squares): The diagonal of a parallelogram divides it into two congruent triangles (by SSS or SAS congruence, as opposite sides are equal and the diagonal is common).
• Isosceles Trapezoid? No—trapezoids (except some special cases) do not have diagonals that create congruent triangles.
• Kite? No—kites have one diagonal that splits into two congruent triangles, but the other does not (unless it’s a rhombus).

Step 2: Analyze Each Figure

• Figure A (Trapezoid): A trapezoid with non-parallel sides unequal. Its diagonals do not form two identical triangles.
• Figure B (Parallelogram): A parallelogram (e.g., rhombus/parallelogram). Its diagonal splits it into two congruent triangles.
• Figure C (Rectangle): A rectangle is a parallelogram. Its diagonal splits it into two congruent right triangles.
• Figure D (Parallelogram?): Appears to be a parallelogram (opposite sides parallel/equal). Its diagonal splits into two congruent triangles.
• Figure F (Kite/Non-Parallelogram?): Likely not a parallelogram; its diagonal does not form two identical triangles.

Thus, the quadrilaterals that can be decomposed into two identical triangles with one line are B, C, and D (assuming D is a parallelogram, B is a parallelogram, and C is a rectangle/parallelogram).

Answer:

B, C, D (select the figures labeled B, C, and D, as they are parallelograms/rectangles whose diagonals split them into two identical triangles).