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CT 107 Homework #18 Answer Coversheet
Q2. Corresponding sides and angles are a pair of matching angles or sides that are in the
same spot in two different shapes.
In Triangle KMH and KPL,
It is given,
∠KMH and ∠KPL are 105 degree
∠MKH = 28 degree
Therefore, ∠KHM = 180 – (105+28) = 47 degree
∠LKP = 75 – 28 = 47 degree
∠PLK = 180 – (47+105) = 28 degree
Corresponding Angles are:
Length of sides are;
KM = 11.5 in., HM = 6.5 in., PM = 5 in.
Therefore, KP = KM – PM = 6.5 in.
Corresponding Sides are:
Q4. Corresponding sides and angles are a pair of matching angles or sides that are in the
same spot in two different shapes.
In Triangle CAB and CDE,
It is given,
∠CAB and ∠CDE are 90 degree
Therefore, corresponding angles are:
Length of sides of Triangle CAB and CDE are,
BC = CE = 6m
Therefore, corresponding sides are:
Q6. If two polygons are similar, we know the lengths of corresponding sides are proportional. In similar polygons, the ratio of one side of a polygon to the corresponding side of the other is called the scale factor.
Corresponding sides are,
FG = (11.4 * 7.8) / 9.5 = 9.36
FK+JK+GH+FG+HJ = 10.32+12.84+12.24+9.36+11.4 = 56.16
Q8. Given angles ∠G = ∠J, ∠F = ∠H
Side FG corresponds to JH,
FK corresponds to MH,
MJ corresponds to GK
Scale factor is FG / JH = 9.92/6.2 = 1.6
Q10. Let us divide triangle into a left section and right section.
Scale factor of triangle on right side is 8ft/5ft
Scale factor of triangle on left side is 12ft/7ft
For a polygon to be convex, all of its interior angles must be less than 180 degrees. Otherwise, the polygon is concave.
Q1. Convex Polygon
Q2. Convex Polygon
Q3. Not a Polygon
Q4. Concave Polygon
Q5. Convex Polygon
Q6. a. Equiangular Polygon since all of its angles are equal to 108 degrees
Q8. a. Equilateral Polygon since all of its sides are equal to 8 cm
All sides have equal length for a rhombus. It is given that CD =3.7 in. Therefore, CB is 3.7 in.
Opposite sides are equal for a parallelogram. It is given ∠S is 80.45 degree and ∠M is opposite to ∠S. Therefore, ∠M is 80.45 degree.
∠SPT = 72.08 degree ∠PST = 80.45 degree
∠STP = 180- (∠SPT+∠PST) = 180 – (72.08+80.45) = 180 – 152.53 = 27.47 degree
∠STM = ∠STP + ∠MTP = 27.47 + 72.08 = 99.55 degree
There are four triangles in hexagon and because the sum of the angles of each triangle is 180 degrees. We get, 4* 180 = 720
Number of degrees in the sum of the interior angles of hexagon =720 degrees
the measure of the angle of a regular 9-sided polygon is 140 degrees.
the sum of all the interior angles is (9 * 140) = 1260 degrees
There are ten triangles and because the sum of the angles of each triangle is 180 degree.
Number of degrees in the sum of the interior angles of a 12-sided polygon = 1800 degree.
Fifth angle of the pentagon = 540 – (97+142+76+103) = 122 degree
Eight angle of the octagon = 1080 – (94+157+132+119+163+170+127) = 118 degree
Q18. The exterior angles of any regular polygon must add up to 360°.
Number of sides of each regular polygon having an exterior angle;
360/12 = 30 sides
360/22.5 = 16 sides
360/3°45`= 104 sides (approx.)
Q22. A median of a trapezoid is the segment that joins the midpoints of the nonparallel sides (legs). Theorem: The median of a trapezoid is parallel to each base and the length of the median equals one-half the sum of the lengths of the two bases.
Median = 1/2 * (21.6 + 36.2) = 28.9 cm
Median = 1/2 * (14’9’’+20’7’’) = 1/2 * (35’4’’) = 17’8’’
AO = 13’2’’ – 9’2’’ = 4 ft = 48 in.
Consider triangle ABO and AEG,
Both the triangles are similar,
Using Pythagoras theorem:
Since the trapezium is isosceles AG = HD
Therefore HD = AG = 24 in.
Since the trapezium is isosceles non-parallel sides are equal in length,
AB = CD = 58.24 in
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