Constructions 6
Name:____________________________
Date:______________
OBJECTIVE: SWBAT copy an angle using constructions.
OPENING EXERCISE
In the following figure, circles have been
constructed so that the endpoints of the diameter
of each circle coincide with the endpoints of each
segment of the equilateral triangle.
A. What is special about points 𝑫, 𝑬, and 𝑭?
Explain how this can be confirmed with the
use of a compass.
B. Using a straightedge, draw DE, EF, and FD. What kind of triangle must △ DEF
be?
C. What is special about the four triangles within △ ABC?
D. How many times greater is the area of △ ABC than the area of △ CDE?
Page 1 of 7
Constructions 6
HOW
TO
COPY
AN
ANGLE
[You will need a compass and a straightedge]
FOLLOW
THE GIVEN STEPS TO COPY THE ANGLE:
1. Label the vertex of the original angle as 𝑩.
⃗⃗⃗⃗⃗ as one side of the angle to be drawn.
2. Draw 𝑬𝑮
3. Draw an arc from vertex 𝑩, any size through the angle.
4. Label the intersections of the arc with the sides of the angle as 𝑨
and 𝑪.
5. Draw an arc of same size from point E.
⃗⃗⃗⃗⃗ as 𝑭.
6. Label intersection of the arc with 𝑬𝑮
̂.
7. Draw an arc from point F, the same span size as 𝑪𝑨
8. Label intersection of arcs as 𝑫.
9. Draw ⃗⃗⃗⃗⃗⃗
𝑬𝑫.
Page 2 of 7
Constructions 6
Copy the given angle and measure both angles to confirm.
Given
Copy
1.
What is the measure of the angle?____
2.
Page 3 of 7
What is the measure of the angle?____
Constructions 6
COPY
THE GIVEN FIGURE IN THE BOX INTO THE NEXT BOX.
3.
COPY
4.
COPY
5.
COPY
Page 4 of 7
Constructions 6
6. Using your knowledge of copying an angle, construct a line parallel to the line
through point A.
1. Draw a diagonal line through A
2. Draw an arc from the lower angle
3. Copy the arc from A intersecting the diagonal line at “B”
4. Measure the 1st arc
5. Put center at “B” and copy the arc intersecting at “C”
6. Connect A to the intersection at “C”
A
ℓ1
7. Construct a line parallel to the line through point A.
A
ℓ1
Page 5 of 7
Constructions 6
Problem Set
1. Which construction of parallel lines is justified by the theorem “If two lines are
cut by a transversal to form congruent alternate interior angles, then the lines are
parallel.
1.
2.
3.
4.
2.The diagram shows the construction of a line
m, parallel to line l, through point P. Which
theorem was used to justify this construction?
1. If two lines are cut by a transversal and the alternate interior angles are
congruent, then lines are parallel.
2. If two lines are cut by a transversal and the interior angles on the same side are
supplementary, the lines are parallel.
3. If two lines are cut by a transversal and the corresponding angles are congruent,
they are parallel.
4. If two lines are perpendicular to the same line they are parallel.
⃡⃗⃗⃗⃗ through point P.
3. The diagram illustrates the construction of ⃡⃗⃗⃗
𝑃𝑆 parallel to 𝑅𝑄
Which statement justifies this construction?
1) m<1 = m<2
Page 6 of 7
2) m<1 =m<3
̅̅̅̅
̅̅̅̅ ≅ 𝑅𝑄
3) 𝑃𝑅
̅̅̅̅ ≅ 𝑅𝑄
̅̅̅̅
4) 𝑃𝑆
Constructions 6
4. The diagram shows the construction of ⃡⃗⃗⃗⃗
𝐴𝐵 through point P parallel to ⃡⃗⃗⃗⃗
𝐶𝐷. Which
theorem justifies this method of construction?
1. If two lines in a place are perpendicular to a transversal at different points, then
the lines are parallel.
2. If two lines in a plane are cut by a transversal to form congruent corresponding
angles, then the lines are parallel.
3. If two lines in a place are cut by a transversal to form congruent alternate
interior angles, then the lines are parallel.
4. If two lines in a place are cut by a transversal to form congruent alternate
exterior angles, then the lines are parallel.
5. Using a compass and straightedge, construct a line parallel to the line through
point A.
A
ℓ1
Page 7 of 7