Use the image to answer the question. Select the correct decomposition of triangle ABC into triangles. Choose 1 for Figure A , 2 for Figure B , or 3 for both Figure A and Figure B . (1 point)
Without an image, I cannot accurately answer the question. However, if there is a triangle ABC in the image, I would need to see it in order to analyze and provide the correct decomposition of the triangles.
Triangle Decomposition of Polygons Quick Check 1 of 51 of 5 Items Question Use the image to answer the question. Choose the correct decomposition of the regular polygon into n−2 triangles. (1 point) Responses Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles. Figure 2 is the correct decomposition because Figure 2 is decomposed into 5 triangles. Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles. Figure 1 is the correct decomposition because Figure 1 is decomposed into n minus 2 equals 5 minus 2 equals 3 triangles. Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into triangles that are equal sizes. Figure 2 is the correct decomposition because Figure 2 is decomposed into n−2 triangles.
Based on the given options, the correct answer would be:
Figure 1 is the correct decomposition because Figure 1 is decomposed into n−2=5−2=3 triangles.
Use the image to answer the question. Choose the correct decomposition of the polygon into n−2 triangles. (1 point) Responses Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into 2 triangles that are equal sizes. Figure 2 is the correct decomposition because it has n−2=4−2=2 triangles. Figure 2 is the correct decomposition because it has n minus 2 equals 4 minus 2 equals 2 triangles. Figure 1 is the correct decomposition because it has 4 triangles of the equal size. Figure 1 is the correct decomposition because it has 4 triangles of the equal size. Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes. Figure 1 is the correct decomposition because Figure 1 is decomposed into 4 triangles that are not equal sizes. Skip to navigation
To accurately answer the question, I would need to see the provided image showing the polygon that needs to be decomposed into n-2 triangles. Without the visual representation, I am unable to determine the correct decomposition.
Triangle Decomposition of Polygons Quick Check 3 of 53 of 5 Items Question Use the image to answer the question. Is this the correct decomposition of a honeycomb shaped like a hexagon into n−2 triangles? (1 point) Responses No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles. No, this is not the correct decomposition because the decomposition is 4 equal-sized triangles. Yes, this is the correct decomposition because the decomposition is 6 triangles. Yes, this is the correct decomposition because the decomposition is 6 triangles. Yes, this is the correct decomposition because the decomposition has n−2=6−2=4 triangles. Yes, this is the correct decomposition because the decomposition has n minus 2 equals 6 minus 2 equals 4 triangles. No, this is not the correct decomposition because the decomposition is 4 triangles. No, this is not the correct decomposition because the decomposition is 4 triangles.
Without the provided image, I am unable to determine the correctness of the decomposition of a honeycomb shaped like a hexagon into n-2 triangles.
Use the angle sum of triangles to develop the interior angle sums of regular polygons formula using decomposition. Test the formula by finding the sum of the interior angles of a square.(1 point) Responses The sum of the angles of a square is 1,440°. The sum of the angles of a square is 1,440 degrees . The sum of the angles of a square is 182°. The sum of the angles of a square is 182 degrees . The sum of the angles of a square is 360°. The sum of the angles of a square is 360 degrees . The sum of the angles of a square is 1,080°.
First, let's decompose the square into four congruent triangles by drawing a diagonal from one corner of the square to the opposite corner. This creates two triangles in the upper half of the square and two triangles in the lower half.
Each of these triangles is an isosceles triangle, meaning that two of its sides are equal in length. In this case, the two congruent sides are the sides of the square, so each angle at the apex of the triangle is a right angle (90°). The remaining angle of each triangle is a base angle.
Since the sum of the interior angles of a triangle is always 180°, each base angle of the triangle in the square is equal to (180° - 90°) / 2 = 45°.
To find the sum of the interior angles of a square, we need to add up the measures of all the interior angles of the four triangles.
Since each triangle has two base angles of 45°, the total measure of the base angles in the four triangles is 4 * 45° = 180°.
Since the sum of the interior angles of a square is equal to the sum of the measures of its base angles, the sum of the interior angles of a square is also 180°.
Therefore, the correct answer is:
The sum of the angles of a square is 180°.