Question

lesson 4: construction techniques 2: equilateral triangles
cool down: i’m stuck in a circle! help!

1. use straightedge and compass moves to create an equilateral triangle. lightly shade the triangle to make it easier to see.
2. fill in the blank based on the following diagram:

\\(\overline{ao}\\) is congruent to segment __ i know this because__.

1. this makes \\(\triangle oab\\):

a. equilateral
b. isosceles
c. scalene

Explanation:

Step1: Construct an equilateral triangle

1. Draw a line segment \(AB\) using a straight - edge.
2. Place the compass at point \(A\), set the width of the compass to the length of \(AB\), and draw an arc.
3. Place the compass at point \(B\), set the width of the compass to the length of \(AB\), and draw an arc that intersects the previous arc at point \(C\).
4. Connect points \(A\) and \(C\), and points \(B\) and \(C\) using a straight - edge. Shade \(\triangle ABC\).

Step2: Analyze congruent segments in a circle

In a circle with center \(O\), if \(A\) and \(B\) are points on the circle and \(O\) is the center, \(\overline{AO}\) is congruent to segment \(\overline{BO}\) because all radii of a circle are congruent.

Step3: Classify the triangle

Since \(O\) is the center of the circle and \(A\) and \(B\) are on the circle, \(OA = OB\). So, \(\triangle OAB\) is isosceles.

Answer:

1. Follow the above - described construction steps to draw an equilateral triangle.
2. \(\overline{AO}\) is congruent to segment \(\overline{BO}\) because all radii of a circle are congruent.
3. b. Isosceles