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WEEK 9 (assignments 30-33)
10/25 homework #30 Constructing triangles
SSS, given the sides, construct the triangle
(a)AB=BC=CA (one original length)
(b)AB=BC and CA<2AB (two original lengths)
(c)AB‚BC‚ CA (three original lengths two shortest must sum to more than the longest)
(d)AB, BC=2AB and CA=2-1/2AB (three original lengths)
(e)AB, BC=1/2AB and CA=2AB (three original lengths)
10/26 homework #31 Constructing triangles
SAS, given two sides and the included angle
(a) Acute angle A, and AB=AC
(b) Acute angle A, and AB≠AC
(c) Obutuse A, and AB≠AC
(d) Obtuse angle A, and AC=2AB
(e)
Right angle A, and AC=1/2AB
(EC) Angle A and AB≠BC (note: Both of the sides are not on angle A)
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.
10/28 homework #32
Construct These angles by combining 60 and 90 degree angles, and their bisections and
quadrasections. Label the angles with three letters and box the statement showing the
measure is equal to the values below:
15, 10, 45, 60, 75, 90, 105, 120, 135, 150, 165
Below are some hints to get to the new angles
by adding these pairs:
(1) 45+60 (2) 45+30 (3) 45+15 (4) 90+60 (5) 90+15
Construct new angles by subtracting these pairs:
(6) 180-15 (7) 90-60 (8) 90-30
EC: 90+60-45.
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.
10/29 homework (see below)*
11/01 homework (#34)*
(note this homework was assigned on 11/01-week 10)
Construct a total of five (5) 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.
(1)
ΔABC with AC=2AB,BC=1½AB
(2)
ΔABC with mB = 90 degrees by “pulling a right angle from a point ON the line”, AC=2AB
(3)
ΔDEF with mE = 45 degrees by bisecting a 90, EF= ½ED
(4)
ΔGHI with mH = 60 degrees by using the “equilateral triangle” method, GI=2GH
(5)
ΔJKL with mK = 30 degrees by bisecting a 60, KL= ¼KJ
Note Label all the points and congruent parts on the image construction
*10/29 homework
OAR’s on-line assessment worth a double homework (due 11/4):
Online OARs common assessment pretest (20 POINTS).
Go to the OARs link and click on the Geometry Ch 4-6 Cumulative Practice Pre-Test .
finished by the close of the window on Thursday 11/4 at 7:00am.
https://secure.oarsaccess.net/fremont/_oa/online_assessment.php?jump=y
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