Question

1. in the diagram, line (ac) is parallel to line (df). which angle is vertical to (angle deh)? a. (angle abe) b. (angle bef) c. (angle gbc) d. (angle hef) 2. consider the pre - image and image of a polygon, which are similar by a sequence of transformations. which statement best explains why the pre - image of the polygon is similar to the image of the polygon? a. the image of the polygon has congruent angle measurements but different side lengths as its pre - image. b. the image of the polygon has congruent side lengths and angle measurements as its pre - image. c. the image of the polygon has different angle measurements but congruent side lengths as its pre - image. d. the image of the polygon has different side lengths and angle measurements as its pre - image.

Explanation:

Question 1

Step1: Recall vertical - angle definition

Vertical angles are formed by two intersecting lines and are opposite each other.

Step2: Identify intersecting - lines and vertical angles

Lines \(AC\) and \(DE\) intersect at point \(B\). \(\angle DEH\) and \(\angle BEF\) are vertical angles because they are formed by the intersection of the lines that contain the rays forming these angles.

Step1: Recall the definition of similar polygons

Similar polygons have the same shape, which means their corresponding angles are congruent and their corresponding side - lengths are in proportion (not congruent in non - congruent similar cases).

Step2: Analyze each option

• Option A: The image of the polygon has congruent angle measurements but different side lengths as its pre - image. This is the correct property of similar polygons.
• Option B: Similar polygons do not have congruent side lengths (except in the case of congruent polygons which are a special type of similar polygons).
• Option C: Similar polygons have congruent angles, not different angle measurements.
• Option D: Similar polygons have congruent angles, not different angle measurements.

Answer:

B. \(\angle BEF\)

Question 2