Question

1. which construction could be used to construct an isosceles triangle abc given line segment ab? a. mark a third point c not on segment ab. draw segments ac and bc. b. label a point c on segment ab and construct a line perpendicular to ab through point c. draw segments ac and bc. c. construct the perpendicular bisector of segment ab. mark the intersection of this line and ab and label it c. draw segments ac and bc. d. construct the perpendicular bisector of segment ab. mark any point c on the perpendicular bisector except where it intersects ab. draw segments ac and bc. 5. select all true statements about regular polygons. a. all angles are right angles. b. all angles are congruent. c. all side lengths are equal. d. there are exactly 4 sides. e. there are at least 3 sides. (from unit 1, lesson 7.)

Explanation:

Step1: Recall isosceles - triangle property

An isosceles triangle has two equal - length sides. The perpendicular bisector of a line segment has the property that any point on it is equidistant from the two endpoints of the line segment.

Step2: Analyze option D

If we construct the perpendicular bisector of segment $AB$ and mark any point $C$ on the perpendicular bisector (except where it intersects $AB$), then by the property of the perpendicular bisector, $AC = BC$. So, $\triangle ABC$ is an isosceles triangle.

Step3: Recall regular - polygon definition

A regular polygon is a polygon that is equiangular (all angles are congruent) and equilateral (all side - lengths are equal). Also, a polygon has at least 3 sides.

Step4: Analyze regular - polygon statements

• Option A: Not all regular polygons have right angles. For example, a regular hexagon does not have right angles.
• Option B: By definition, all angles of a regular polygon are congruent.
• Option C: By definition, all side - lengths of a regular polygon are equal.
• Option D: Regular polygons can have more than 4 sides (e.g., a regular pentagon has 5 sides).
• Option E: A polygon is defined as a closed - figure with at least 3 sides, and a regular polygon is a type of polygon.

Answer:

1. D. Construct the perpendicular bisector of segment $AB$. Mark any point $C$ on the perpendicular bisector except where it intersects $AB$. Draw segments $AC$ and $BC$.
2. B. All angles are congruent.

C. All side lengths are equal.
E. There are at least 3 sides.