Constructing Congruent Angles with Compass and Straightedge

What is the primary purpose of using a compass in constructing congruent angles?

• To erase mistakes

• To draw straight lines

• To draw perfect circles or arcs of a given radius

• To measure the length of lines

What do you call the point where the compass pivots?

• Vertex

• Center

• Pivot point

• Radius

What is the first step in constructing a congruent angle?

• Measuring the distance between points

• Making the vertex of the second angle

• Drawing an arc with the compass

• Drawing the second ray

Why is it important to keep the radius constant when drawing the arc with the compass?

• To make the construction faster

• To draw a larger arc

• To make sure the arc intersects the rays at the correct points

• To ensure the arc is a perfect circle

What is the purpose of drawing the first arc in the construction?

• To intersect the rays at specific points

• To measure the angle

• To find the midpoint

• To draw the second ray

How do you determine where to place the third point (F) when constructing the second ray?

• By guessing its position

• By measuring the distance between points B and C

• By using a ruler

• By drawing another arc

What is the significance of the distance between points B and C in the construction?

• It ensures the angles are congruent

• It determines the length of the second ray

• It is used to draw the arc

• It helps in drawing the first ray

What is the final step in ensuring the angles are congruent?

• Drawing the second ray

• Measuring the distance between points

• Drawing an arc

• Comparing the triangles formed

Which property of triangles is used to verify that the angles are congruent?

• The area of the triangles

• The sum of the angles

• The length of the sides

• The perimeter of the triangles

Why is it not recommended to use a pen for this construction?

• Mistakes cannot be erased

• It is difficult to see

• It is not precise

• It cannot draw straight lines