Triangle A B C is reflected across BC and then is rotated about point C to form triangle D E C.
1) Since SSS Postulate states that if the three sides of one triangle have the same measure as another triangle then both triangles are congruent.
<h3>
What is the consequence postulate?</h3>
The consequence of this Postulate is that these triangles have respectively the same angles.
We have given that,
Triangles A B C and D E C are connected at point C.
Triangle A B C is reflected across BC and then is rotated about point C to form triangle DEC.
2) Notice below both triangles SSS, an example, in this case, an isosceles triangle, firstly reflected (grey one ) then rotated by point C.
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Answer:
Dimension of room = 18 foot x 18 foot
Step-by-step explanation:
Let the square room is of side a foot,
The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot
Total cost is $1773.
Cost for re-finishing the hardwood floors = Area x 2.25
Area = a²
Cost for re-finishing the hardwood floors = 2.25 a²
Cost of purchasing and installing the new baseboards = Perimeter x 14.5
Perimeter = 4a
Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a
Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards
1773 = 2.25 a² + 58a
2.25 a² + 58a - 1773 = 0
a = 18 or a = -43.77(not possible)
Dimension of room = 18 foot x 18 foot
S = r*θ . . . . where θ is in radians
s = (15 in)*(100°*π/180°)
s = 25π/3 in ≈ 26.18 in
Answer:
0.6625 in²
Step-by-step explanation:
The surface area of this figure will be the area of the base added to area of the triangles
Area of the 4 triangles
Area of a triangle is given by ;
![A=\frac{1}{2} *b*h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%2Ab%2Ah)
where b is the base length and h is the height of the triangle
<u>Area of 1 triangle</u>
Given base length as 0.25 inches and height is 1.2 inches.
![A=\frac{1}{2} *0.25*1.2=0.15\\](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%2A0.25%2A1.2%3D0.15%5C%5C)
Area of all 4 triangles
- multiply the area of one triangle by 4
- 0.15*4=0.6 in²
<u>Area of the base</u>
The base is a square of length 0.25 inches
Area of a square=length×length
![A=l*l\\A=0.25*0.25=0.0625in^{2}](https://tex.z-dn.net/?f=A%3Dl%2Al%5C%5CA%3D0.25%2A0.25%3D0.0625in%5E%7B2%7D)
<u>Total surface area</u>
Total surface area= Area of the triangles + Area of the base
![=0.6+0.0625=0.6625in^{2}](https://tex.z-dn.net/?f=%3D0.6%2B0.0625%3D0.6625in%5E%7B2%7D)