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Constructions Flipbook PDF
Constructions: 1.2 Perpendiculars In this section, we will discuss three different cases for constructing perpendicular
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Constructions: 1.2 Perpendiculars In this section, we will discuss three different cases for constructing perpendicular lines. CONSTRUCTION #4: Construct the perpendicular bisector of a given segment. Given AB , construct the perpendicular bisector. 1. Choose any convenient setting that is 1 more than AB . C 2 2. Set the compass at A and draw an arc through AB . 3. Keep the same setting, put the compass at B and draw an arc that intersects the previous arc both above and below the A given segment. Label these points C and D.
B
4. Use a straightedge to draw CD . 5. CD is the perpendicular bisector of AB . D
CONSTRUCTION #5: Given a point on a line, construct a line through the point, perpendicular to the given line. Given point F on line l, construct a perpendicular at F. 1. Set the compass at F and draw two arcs on line l of M equal distance on either side of F. Label these H and K. 2. Using a LARGER setting for the compass, put the compass at H and draw and arc above the line. 3. Using the same setting, put the compass at K and l draw an arc that intersects the previous arc. Label F K H this intersection point M. 4. Use a straightedge to draw MF . 5.
MF is perpendicular to line l at F.
NOTE!! Construction #4 is applied when we need to find the midpoint of a segment. NOTE!! Construction #5 is the same as problem #6 in Lesson 1. The bisector of a straight angle is a perpendicular line.
CONSTRUCTION #6: Given a point not on a line, construct a line through this point perpendicular to the given line. Given line m and point P (not on line m), construct a line P through P perpendicular to m. 1. Set compass at P and draw any arc that intersects line m in two points. Label these Q and S. 2. Set compass at Q, draw an arc below the line. 3. Using the same setting, put compass at S and draw an Q arc that intersects the previous arc. Label this T.
m S
4. PT is perpendicular to line m. T NOTE!!: Construction #6 is applied when we need to construct the altitude of a triangle. Point P would be the vertex angle and the line would be the base of the triangle (extended when needed). ASSIGNMENT: 1. Construct the perpendicular bisector of AB and CD .
A
C
B
D
2. Construct a line through G and H perpendicular to PQ and RS .
P
G
Q
R
H
S
3. Construct a line through J and K perpendicular to AB and CD . J
A
K
B C
D
4. Determine the midpoint of FL and HL . L
H
F
5. Construct the median from R to side ST . R
S
T
6. For ∆ ABC , construct the three altitudes to each side. What appears to be true?
A
C
B
7. Construct the ⊥ bisectors for each side. Extend until they cross. Measure the distance from this point to each vertex. What seems to be true?
D
E
F