Unit 2 Lesson 4: Constructing Angles

Question 1

arc

Answer 1

a continuous portion (as of a circle or ellipse) of a curved line or a curved path

Question 2

angle

Answer 2

a figure formed by two rays extending from the same point

Question 3

auxiliary line

Answer 3

an extra line needed to construct other figures in geometry

Question 4

vertex

Answer 4

a point (as of an angle, polygon, polyhedron, graph, or network) that terminates a line or curve or comprises the intersection of two or more lines or curves

Question 5

congruent

Answer 5

identical in both size and shape

Question 6

angle bisector

Answer 6

a line or segment that divides an angle into two equal parts

Question 6

Describe how to construct an angle using a straightedge.

Answer 6

Draw a point on a piece of paper and then construct two rays with the same endpoint going in different directions.

Question 7

In addition to two rays (or lines or segments), what other feature is necessary to form an angle?

Answer 7

The other feature necessary for forming an angle is a vertex point.

Question 8

How to construct a congruent angle

Answer 8

• Draw an angle and then draw an auxiliary line somewhere else that is long enough.
• Place a point at one end of the auxiliary line.
• Using a compass, draw an arc on the original angle and place points at the intersection with the rays and arc.
• Keeping the compass at the same distance, draw another arc on the auxiliary line that is just larger than the original arc.
• Place another point on the auxiliary line where the arc intersects with the auxiliary line. Measure the distance between the two points on the sides of the angle of the original angle using your compass.
• Place the compass on the new point on the auxiliary line and draw a small arc that intersects with the large arc and place a point there.
• Finally draw a ray from the vertex point to the new point placed.

Question 9

Using paper, a pencil, and a straightedge, construct an angle bisector.

Answer 9

• Draw an angle using a straightedge with vertex point A.
• Using a compass, draw an arc that intersects both sides of the angle.
• Place two points at the intersection of the arc with both sides of the angle.
• Placing the pointed end of the compass on one of the two points of intersection, draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.
• Placing the pointed end of the compass on the other point of the two points of intersection, draw a smaller arc inside the angle that extends more than halfway across the inside of the angle.
• Place a point at the intersection of the two smaller arcs and draw a ray from the vertex point through the point you just placed.