An illustration shows a 13 by 9 grid with 4 triangles and a rectangle on it. Figure A is a right triangle that extends from the top of the 2nd to the end of the 3rd rows, in the 3rd column. The base is 1 unit wide along the bottom of row 3 in column 3, and the perpendicular line is 2 units high the left side of column 3. Figure B is a right triangle with a base that runs 6 units along the bottom of row 4 from column 7 through column 12. The perpendicular edge runs 3 units along the left edge of column 7, from row 2 to 4. Figure C, a rectangle, covers the 5th and 6th row units in column 2. Figure D, an inverse right triangle, extends from the top of the 6th to the end of the 8th rows, in column 5. The base occupies the top of 6th row for 1 unit, and the perpendicular line for 3 units on right side of the 5th column. Figure E, a right triangle, extends from the top of 6th to the end of the 8th rows, in columns 9 and 10. The base occupies the bottom of 10th row for 2 units and the perpendicular line runs for 3 units on the left side of column 9.Which figure can you describe as similar to Figure A?

Answer 1

To determine which figure is similar to Figure A, we need to analyze the dimensions of Figure A as well as the dimensions of the other figures in the grid.

Figure A:

• It's a right triangle.
• Base: 1 unit (along the bottom of row 3 in column 3).
• Height: 2 units (along the left side of column 3).

Dimension Ratios for Figure A:

• Base: 1
• Height: 2
• The ratio of height to base is \( \frac{2}{1} = 2 \).

Now let's analyze the other figures for similarity.

Figure B:

• It's also a right triangle.
• Base: 6 units (along the bottom of row 4 from column 7 to column 12).
• Height: 3 units (along the left side of column 7 from row 2 to row 4).
• Ratio: \( \frac{3}{6} = \frac{1}{2} \). This is not the same ratio as Figure A.

Figure C:

• It's a rectangle and does not match the definition of a triangle and thus cannot be similar.

Figure D:

• It's an inverse right triangle (which is technically still a triangle).
• Base: 1 unit (along the top of row 6 in column 5).
• Height: 3 units (along the right side of column 5).
• Ratio: \( \frac{3}{1} = 3 \). This is not the same ratio as Figure A.

Figure E:

• It's a right triangle.
• Base: 2 units (along the bottom of row 10 in columns 9 and 10).
• Height: 3 units (along the left side of column 9).
• Ratio: \( \frac{3}{2} = 1.5 \). This is not the same ratio as Figure A.

Upon comparing all the figures, none of them have the same ratio of height to base (2:1) as Figure A. Therefore, it can be concluded that none of the figures are similar to Figure A based on their dimensions and ratios.