Construction: Draw a ray with its endpoint on the left. Label this point B.

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1 Name: Ms. Ayinde Date: Geometry CC 1.13: Constructing Angles Objective: To copy angles and construct angle bisectors using a compass and straightedge. To construct an equilateral triangle. Copy an Angle: For this construction, you are learning how to copy the degree measurement of an angle. Step 1: Construction: Draw a ray with its endpoint on the left. Label this point B. Step 2: Place the center of the compass on Point B and slide your slider holes to the right so that you are able to create an arc that intersects with both sides of the angle. Step 3: Move your compass onto point B. Without altering the positioning of the slider, place you pencil in the slider hole and create a long arc starting above the ray and intersecting then with ray. Step 4: Place you compass on one of the intersection points between the arc and the original angle. Place the hole of the slider over the second intersection. You are using the compass to measure the distance between these two intersection points. Step 5: Without altering the compass settings. Slide the center of the clear circle over the point of intersection between the ray you drew and the arc intersecting it. Create an arc that intersects with the arc already drawn. What is the relationship between these two angles? Step 6: Draw a line from point B to the point of intersection for those arcs. Do not erase any of your construction marks!

2 Bisect an angle: For this construction, you are learning how to bisect an angle by constructing an angle bisector. Construction: Step 1: Place the compass point on the vertex of the angle. Create an arc that intersects both sides of the angle. Step 2: Without changing the settings of the compass, place the compass point on one of the intersections between the arc and the angle. Draw a nice big arc within the interior of the angle. Step 3: Without changing the settings of the compass, place the compass point on the second intersection between the arc and the angle. Draw a nice big arc within the interior of the angle. Step 4: Your two arcs should intersect. Using your straightedge, you are going to draw a ray starting from the vertex B going through the intersection point between the two arcs. Label this point of intersection D What is the relationship between these two small angles? What is the relationship between the three angles?

3 Construct an Equilateral Triangle: For this construction, we will create an equilateral triangle. Step 1: Place the center of the clear circle on point A and slide your slider on point B. Create a large arc. Construction: Step 2: Without changing the settings, place your clear circle on Point B and create a large arc. Step 3: The two arcs will intersect. This intersection is the third vertex of the triangle. Label it C. Step 4: Using your straightedge, connect A with C. Then connect B with C. Do not erase any of your construction marks! What is the relationship between the three sides of the triangle.

4 Practice: Leave all your construction marks. 1. Construct an obtuse angle below. Label this PHD. Using your straightedge and compass copy the angle and label the new angle P H D. 2. Construct an acute angle without using your protractor. Label the acute angle HOP. Using a compass and straightedge, construct angle bisector OG. Write a congruence statement about the two angles. 3. Construct an equilateral triangle whose side is equal in length (congruent to) the segment AB. Write a congruence statement about the three sides of the triangle.

5 4. Construct an acute angle. Label this SIP. Using a compass and straightedge, construct angle bisector IT. a. Write a congruence statement about the two small angles and an addition statement about the three angles. b. If m SIT = 5x + 4 and m TIP = 3(x 4), what is the m SIP? Justify every step you take when solving.

6 5. Create and equilateral triangle with sides that are each 5 cm long. Label the triangle ABC. a. Write a congruence statement about the three sides of the triangle. b. If AB = x+2, BC = 3x-4, and CA = 11-2x, determine the value of x.