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Answer:
The measure of angle C is
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent
In this problem
m<A=m<D
m<B=m<E
m<C=m<F
we have that
so
m<B=m<E
Remember that
The sum of the interior angles in a triangle must be equal to 180 degrees
substitute values and solve for m<C
If points D, E, F and G make a rectangle with the given coordinates for each point then the area of the rectangle is 150 sq. units
How to find distance between two points?
Distance between two points is the length of the line segment that connects the two points in a plane.
The formula to find the distance between the two points is usually given by D = √((x₂ – x₁)² + (y₂ – y₁)²)
This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
According to the given question:
The four vertices are D(-1,-3), E(-9, -9), F(-18, 3) and G(-10, 9) check the attachment below.
Distance between two points D = √((x₂ – x₁)² + (y₂ – y₁)²)
Side DE = √((-9 – (-1))² + (-9 – (-3))²) = √100 = 10 units
Side EF = √((-18 – (-9))² + (3 – (-9))²) = √225 = 15 units
Side FG = √((-10 – (-18))² + (9 – 3)²) = √100 = 10 units
Side GD = √((-1 – (-10))² + (-3 – 9)²) = √225 = 15 units
∴ Area of rectangle = l x b = DE . EF
Area = 10 x 15 = 150 sq. units
Hence the area of rectangle with the given coordinates is 150 sq. units
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