All three pairs of figures are similar.
Definition of Similarity:
Two figures are said to be similar if they have the same shape, but not necessarily the same size. This means that one figure can be obtained from the other by a combination of transformations, such as translations, rotations, reflections, and dilations.
Step 1: Identify Corresponding Angles:
To determine whether two figures are similar, we need to identify corresponding angles. Corresponding angles are angles that share the same position in each figure. For example, if we have two triangles, the corresponding angles are the angles that have the same name (e.g., angle A in triangle 1 corresponds to angle A in triangle 2).
Step 2: Check for Congruent Angles:
If the corresponding angles of two figures are congruent (have the same measure), then the figures are similar. This is because congruent angles indicate that the figures have the same shape.
Step 3: Check for Equal Scale Factors:
If the corresponding sides of two figures have equal scale factors, then the figures are also similar. A scale factor is a ratio of the corresponding side lengths in two figures. If all corresponding side lengths have the same scale factor, then the figures are said to be dilations of each other.
Applying the Steps:
Using the given information, let's analyze each pair of figures:
Pair 1:
Corresponding angles: <Z = <V (given)
Scale factors: Equal (given)
Since the corresponding angles are congruent and the scale factors are equal, the two figures are similar.
Pair 2:
Corresponding angles: <LSE = <LCE (given), <LTE = <LTC (given)
Scale factors: Equal (given)
Since the corresponding angles are congruent and the scale factors are equal, the two figures are similar.
Pair 3:
Corresponding angles: <AJL = <KJU (given)
Scale factors: Equal (given)
Since the corresponding angles are congruent and the scale factors are equal, the two figures are similar.
Therefore, all three pairs of figures are similar.