Download Section 1.6- Basic Constructions Essential Question: How can we

Section 1.6- Basic Constructions
Essential Question: How can we use special geometric tools to make more accurate
figures?
Do Now:
How is ̅̅̅
𝐺𝐽 related to ∠ FGH?
Vocabulary Review

Perpendicular- two lines that intersect to form _________ angles
Symbol

Diagram of Perpendicular Lines
Perpendicular bisector- bisects a line segment and forms two _____________
parts
o Can be a ________, _____________, or _______ that is perpendicular to the
segment at its __________

Circle the figure that correctly shows a perpendicular bisector.
Construction- the making of a geometric figure using only a ________________ and a
__________________ (no ruler or protractor)
Construction #1- Congruent Segments
Objective: To construct a segment congruent to the given segment.
Steps:
̅̅̅̅
Given: 𝑨𝑩
1. Draw a ray with endpoint C.
2. Open the compass to the length of ̅̅̅̅
𝐴𝐵 .
3. With the same compass setting, put the
compass point on C. Draw an arc that
intersects the ray. Label the point of
intersection D.
Result:
__________ ≅ __________
Construction #2- Congruent Angles
Objective: To construct an angle congruent to a given angle.
Steps:
1. Draw a ray with endpoint S.
2. With the compass point on A, draw an arc
that intersects the sides of ∠A. Label the points
of intersection B and C.
3. With the same compass setting, put the
compass point on point S. Draw an arc that
intersects the ray at point R.
̅̅̅̅ .
4. Open the compass to the length of 𝐵𝐶
Keeping the same compass setting, put the
compass point on R. Draw an arc to determine
point T.
5. Draw ⃗⃗⃗⃗
𝑆𝑇.
Result:
∠ ________ ≅ ∠ _________
Given: ∠A
Construction #3: Perpendicular Bisector
Objective: Construct the perpendicular bisector of a segment.
Steps:
Given: ̅̅̅̅
𝑨𝑩
1. Put the compass point on point A and draw
an arc greater than half the length of the
segment given.
2. Keep the same compass setting, put the
compass point on point B and draw an arc.
Label the points where the two arcs intersect as
X and Y.
̅̅̅̅
3. Draw line XY. Label the intersection of 𝐴𝐵
and ⃡⃗⃗⃗⃗
𝑋𝑌 as point M.
Result:
________ is the perpendicular bisector of
_______. Point M is the _____________ of the
given segment.
Construction #4: Angle Bisector
Objective: Construct the bisector of an angle.
Steps:
1. Put the compass point on vertex A. Draw an
arc that intersects the sides of ∠A. Label the
points of intersection B and C.
2. Put the compass point on point C and draw
an arc. Keep the same compass setting and
repeat with point B. Be sure the arcs intersect.
Label the point where the two arcs intersect as
point X.
⃗⃗⃗⃗⃗ .
3. Draw 𝐴𝑋
Result:
________ is the angle bisector of ∠CAB
Given: ∠A
Construction Practice
1. Congruent Segment
a.
b.
2. Segment Bisector
a.
b.
3. Congruent Angle
a.
b.
4. Angle Bisector
a.
Classwork: Construction Assessment
b.