WEEK 9 (assignments 30-32)
33 is Pretest
Notes on last pages
10/26 homework
Construct a total of five triangles using the methods taught in class for SSS and SAS. Label all
points on the image triangle and three parts that are congruent to the parts in the original side.
using SSS (for 1)
(1) ΔABC with an original AB, making AC=3AB,BC=1½AB (note start with longest side)
using SAS (for 2-5)
(2) ΔDEF with mE = 90 degrees and an original AB making ED=3AB and EF=4AB
(3)
ΔMNO with mN = 45 degrees and an original AB, making MN= 1½AB and NO=2AB
(4)
ΔGHI with mH = 60 degrees and an original AB, making HG=AB and GI=AB
(5)
ΔJKL with mK = 30 degrees and an original AB, making KL= 2AB, and KJ=3AB
Note Label all the points and congruent parts on the image construction
10/27 homework
Construct isosceles triangles given these original parts:
1. Leg, base (therefore all three side)
2. Leg, Vertex angle (acute)
3. Leg, Base = ½ m (Leg)
4. Base, Leg = ½ m (Base)
5. Base, Leg = 2 m (Base)
6. Base angle, Leg (therefore 2 angles , and 2 sides)
7. Base angle, Base
8. Given the vertex angle, find the base angles (by construction)
10/28 homework
Construct two of each of the seven classifications of triangles:
4 types by angles: (a) equiangular, (b) acute, (c) right, (d) obtuse;
3 types by sides: (e) equilateral, (f) isosceles, (g) scalene
A. Equiangular (all angles congruent)
1. Make a ray with one endpoint
2. draw an arc centered at the endpoint thru the ray up to about 90 degrees
3. Without changing the radius place the bull’s eye over the intersection of the ray
and the arc in step 1 and draw an arc thru the first arc.
4. Label and connect the three points: your first endpoint, the intersection of the arc
and the original ray, and the intersection of the two arcs.
(continued)
B. Acute (all angles are acute)
1. Make a ray with one endpoint
2. Construct an angle less than 90 degrees with the endpoint as the vertex.
3. On one of the sides, pick a point as a vertex, and construct an angle that when
added to the angle in step 2 will make an obtuse angle (in class I modeled just
making sure both angles are slightly less than 90 degrees)
4. Extend the side of the second angle to cross the opposite side. Label the
intersections of all three sides.
C. Right (one angle is right)
1. Pull a right angle from a point on a line
2. pick two points on either side of the right angle (the legs)
3. Label and connect the points
D. Obtuse (one angle is obtuse)
1. Make a ray with one endpoint
2. Construct an angle greater than 90 degrees with the endpoint as the vertex.
3. Pick two points on either side of the obtuse angle.
4. Label and connect the points.
E. Equilateral
1. Make a line segments with two endpoints.
2. Span your radius to the length of this one side and draw two arcs, one from each
endpoint that intersection as a point.
3. Label and connect the points.
F. Isosceles
1. Make a point
2. draw an arc about the point
3. pick any two points on the arc
4. Label and connect the points.
G. Scalene
1. Make a line segments with two endpoints.
2. From one endpoint draw a side with a different length as the first at about 90
degrees. Label the endpoint of this new side
3. Label and connect the points.
Reference material from week 8 instructions
SSS Steps
(1) Copy the longest side to the image ray
(2) Span one of the other sides and make an arc from one endpoint of the copied side
in step (1)
(3) Span the last side and make an arc from the other one endpoint of the copied side
in step (1) to intersect the arc made in step (2)
(4) Label the intersection of the arcs in (2) and (3) as the third vertex and connect
the points, labeling congruent sides.
SAS Steps
(1) Copy the angle to the image ray (using the span of the attached side as the
measuring arc radius)
(2) Label the vertex and congruent angle, and label the intersection of the measuring
arc on the image ray as the second vertex.
(3) Span the last side and copy it onto the image angle to interest the other side of
the angle.
(4) Label the intersection of the arc and side as the third vertex and connect the
points, labeling congruent sides.
How to construct a 60 degree angle (using the equilateral triangle method)
1. Make a ray (use point “A” in this example as its endpoint) A
2. Place the bulls-eye over “A” and make an arc to one side of the ray (about ¼ of a circle).
A
3. Without making any adjustments, place the bulls-eye over the intersection of the ¼ circle arc you made in step 2, and the
ray you made in step 1 and make another arc that intersects the arc you made in step 2
4. Place the straight edge from point “A” and the intersections of the two arcs, and make a ray. The two rays make a 60
degree angle.
Reference material from week 7 instructions
How to construct Altitudes from a specified vertex of a triangle, for
the example the construction will be an altitude from vertex “A” on
triangle ABC
(1) Locate the opposite side (for vertex “A”, the opposite side is
the segment with the other two letters of the triangle: CB)
(2) Construct an arc centered at “A” that passes thru the line
collinear to the opposite side in two places(you may need to
extend the opposite side for the arc to pass thru it in two
places)
(3) Make two arcs (with the same radius) from the intersection of
the arc and the line for the opposite side to make an “X”
(similar to the dropping a perpendicular from a point OFF the
line)
(4) Draw line from the “X” in step 3 to vertex “A”
(5) Label the point “Y” where the line in step 4 intersects the
opposite side (or it’s extension) to make segment AY
(6) Make the following statement:
AY is the altitude from vertex A of ∆ABC
How to construct Median from a specified vertex of a triangle, for
the example the construction will be a median from vertex “A” on
triangle ABC
(1) Locate the opposite side (for vertex “A”, the opposite side
is the segment with the other two letters of the triangle:
CB)
(2) Bisect the opposite side (“fisheye”) and make a point at its
midpoint (example label “X”)
(3) Connect the vertex “A” to point “X” to make segment AX
(4) Make the following statement:
AX is the median from vertex A of ∆ABC