Question

1. the diagram below shows the construction of an equilateral triangle. which statement justifies this construction?

a) ( mangle a + mangle b + mangle c = 180 )
b) ( mangle a = mangle b = mangle c )
c) ( ab = ac = bc )
d) ( ab = bc > ac )

1. which construction is represented by these construction marks?

a) copying ( \triangle abc )
b) the perpendicular bisector of ( overline{bc} )
c) the angle bisector of ( angle abc )
d) a perpendicular line to ( overline{bc} )

1. which diagram shows the construction of a ( 45^circ ) angle?

(diagrams labeled a, b, c, d with geometric constructions)

1. segment ( overline{cd} ) is the perpendicular bisector of ( overline{ab} ) at e. which pair of segments does not have to be congruent?

a) ( overline{ae}, overline{be} )
b) ( overline{ac}, overline{bc} )
c) ( overline{ad}, overline{bd} )
d) ( overline{de}, overline{ce} )

Explanation:

Step1: Analyze Question 41

To determine which diagram shows a \(45^\circ\) angle construction, recall that a \(45^\circ\) angle is often constructed by bisecting a \(90^\circ\) (right) angle. A right angle is \(90^\circ\), and bisecting it gives \( \frac{90^\circ}{2}=45^\circ \).

Step2: Evaluate Diagrams

• Diagram A: Likely shows a different construction (e.g., triangle - based, not angle - bisecting a right angle).
• Diagram B: Shows intersecting lines, not a right - angle bisector.
• Diagram C: Shows a right angle (from the perpendicular line) and a bisector of that right angle. The right angle is \(90^\circ\), and the bisector would create two \(45^\circ\) angles.
• Diagram D: Shows intersecting perpendicular lines, creating right angles, but no indication of a \(45^\circ\) angle (no bisector of the right angle shown).

Answer:

The diagram labeled C (the third diagram from the left)