Question

1. the diagram below shows the construction of the perpendicular bisector of ab. which statement is not true? 1) ac = cb 2) cb = (1/2)ab 3) ab = 2ap 4) ab > cb > ac 38. the diagram below shows the construction of an equilateral triangle. which statement justifies the construction? 1) m∠a + m∠b + m∠c = 180 2) m∠a = m∠b = m∠c 3) ab = ac = bc 4) ab + bc = ac 39. the diagram below illustrates the construction of pq parallel to rs through point p. which statement justifies this construction? 1) m∠1 = m∠2 2) m∠1 = m∠3 3) pe = pf 4) rs = pq 40. which construction is represented by these construction marks? a) copying ∠abc b) the perpendicular bisector of ab c) the angle bisector of ∠abc d) a perpendicular line to ab 41. which diagram shows the construction of a 45° angle? (a), (b), (c), (d) diagrams of different angle constructions 42. segment cd is the perpendicular bisector of ab at e. which pair of segments must be congruent? 1) ae ≅ be 2) ce ≅ de 3) ac ≅ bc 4) dc ≅ ec

Explanation:

Step1: Analyze Question 39 (Equilateral Triangle Construction)

An equilateral triangle has all sides equal and all angles equal to \(60^\circ\). So, for \(\triangle ABC\) (assuming the triangle in the diagram), \(m\angle A = m\angle B = m\angle C\) (since each angle in an equilateral triangle is \(60^\circ\)). Let's check the options:

• Option a: \(\angle A+\angle B+\angle C = 180^\circ\) is true for all triangles (angle - sum property), not specific to equilateral.
• Option b: \(m\angle A=m\angle B = m\angle C\) is true for equilateral triangles (all angles equal).
• Option c: \(AB = AC=BC\) is about side lengths, but the question is about justifying the construction. The angle - equality is a key property here.
• Option d: \(AB + BC=AC\) is false for triangles (triangle inequality: \(AB + BC>AC\)).

Step2: Confirm the Correct Option

Since the construction is of an equilateral triangle, the statement that justifies it is the equality of all interior angles, which is \(m\angle A=m\angle B = m\angle C\). So the correct option is b.

Answer:

b. \(m\angle A = m\angle B=m\angle C\)