Discussion on Institutional Affiliation

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CT 107 Homework #18 Answer Coversheet 

 

 

Student’s Name

Institutional Affiliation

Course Name

Professor’s Name

Date

 

 

UNIT 23

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:

  • ∠KMH corresponds to ∠KPL
  • ∠MKH corresponds to ∠PLK
  • ∠KHM corresponds to ∠LKP

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:

  • KP corresponds to HM
  • KH corresponds to LK
  • KM corresponds to LP

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:

  • ∠CAB corresponds to ∠CDE
  • ∠ABC corresponds to ∠DEC
  • ∠ACB corresponds to ∠DCE

Length of sides of Triangle CAB and CDE are,

BC = CE = 6m

Therefore, corresponding sides are:

  • BC corresponds to CE
  • AB corresponds to DE
  • AC corresponds to DC

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,

  • ED and JK
  • AE and FK
  • HJ and CD
  • GF and AB
  • GH and BC
  1. side FG

 

 

FG = (11.4 * 7.8) / 9.5 = 9.36

  1. side GH

 

 

12.24

  1. side JK

 

 

12.84

  1. side FK

 

 

= 10.32

  1. Perimeter of the polygon FGHJK is;

FK+JK+GH+FG+HJ = 10.32+12.84+12.24+9.36+11.4 = 56.16

 

Q8. Given angles ∠G = ∠J, ∠F = ∠H

GK=7.2,

MH=5.5,

Side FG corresponds to JH,

FK corresponds to MH,

MJ corresponds to GK

Scale factor is FG / JH = 9.92/6.2 = 1.6

  • Side FK

 

 

8.8

  • Side JM,

 

11.52

Q10.  Let us divide triangle into a left section and right section.

Scale factor of triangle on right side is 8ft/5ft

5.62

7.5

Scale factor of triangle on left side is 12ft/7ft

8.75

5.25

Unit 24:

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

  1. It is a Pentagon as it has 5 sides.

Q8. a. Equilateral Polygon since all of its sides are equal to 8 cm

  1. It is a pentagon as it has 5 sides

Q10.

  1. side CB

All sides have equal length for a rhombus. It is given that CD =3.7 in. Therefore, CB is 3.7 in.

  1. Opposite sides are equal for a rhombus. It is given that ∠D is 64 degrees and ∠B is opposite to ∠ Therefore, ∠B is 64 degrees.
  2. Opposite sides are equal for a rhombus. It is given that ∠A is 116 degrees and ∠C is opposite to ∠ Therefore, ∠C is 116 degrees.

Q12.

  1. ∠M

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.

  1.  ∠STP

∠SPT = 72.08 degree ∠PST = 80.45 degree

∠STP = 180- (∠SPT+∠PST) = 180 – (72.08+80.45) = 180 – 152.53 = 27.47 degree

  1. ∠SPM

∠SPM =∠STM

∠STM = ∠STP + ∠MTP = 27.47 + 72.08 = 99.55 degree

Q14.

  1. Hexagon

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

  1. 9-sided polygon

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

  1. 12-sided polygon

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.

Q16.

  1. Sum of interior angles of pentagon = (n-2) *180 = (5-2) *180 = 540

Fifth angle of the pentagon = 540 – (97+142+76+103) = 122 degree

  1. Sum of interior angles of octagon = (n-2) *180 = (8-2) *180 = 1080

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;

  1. 12°

360/12 = 30 sides

360/22.5 = 16 sides

  1. 3°45`

360/3°45`= 104 sides (approx.)

 

Q20.

  1. ∠1 = 360° – 66°18’ = 293°82’
  2. ∠2 = 360° – 319°51’ = 40°49’

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.

  1. Bases 21.6 cm and 36.2 cm

Median = 1/2 * (21.6 + 36.2) = 28.9 cm

  1. Bases 14’9’’ and 20’7’’

Median = 1/2 * (14’9’’+20’7’’) = 1/2 * (35’4’’) = 17’8’’

 

Q24.

 

 

AO = 13’2’’ – 9’2’’ = 4 ft = 48 in.

Consider triangle ABO and AEG,

Both the triangles are similar,

Therefore,

 

 

Using Pythagoras theorem:

BA =

 

  1. Distance of AG and HD are;

 

 

AG =

Since the trapezium is isosceles AG = HD

Therefore HD = AG = 24 in.

  1. Length of AB and CD are;

Since the trapezium is isosceles non-parallel sides are equal in length,

Therefore,

AB = CD = 58.24 in

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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