Question

2 points

1. Determine whether the polygons with the given vertices are
similar.Quadrilateral ABCD with vertices A(-5, 4), B(-2, 4), C(-2, 2), D(-5,
2)and quadrilateral EFGH with vertices E(-2, 0), F(4,0), G(4, -6), H(-2,-6)

Answer 1

Step-by-step explanation:To determine whether the polygons with the given vertices are similar, we need to compare the ratios of corresponding side lengths and the ratios of corresponding angle measures.Let's analyze the side lengths of the two quadrilaterals:For Quadrilateral ABCD:

AB = 2 units

BC = 2 units

CD = 2 units

AD = 3 unitsFor Quadrilateral EFGH:

EF = 6 units

FG = 6 units

GH = 6 units

HE = 4 unitsThe corresponding side lengths are not proportional, which indicates that the two quadrilaterals are not similar.To further confirm, we can also compare the angle measures:For Quadrilateral ABCD:

∠A = 90°

∠B = 90°

∠C = 90°

∠D = 90°For Quadrilateral EFGH:

∠E = 90°

∠F = 90°

∠G = 90°

∠H = 90°The corresponding angles are equal in both quadrilaterals, but this alone does not indicate similarity since all right angles are congruent.Based on the analysis of side lengths and angles, we can conclude that the quadrilaterals ABCD and EFGH are not similar.