Helena was curious if quadrilaterals QRSTQRSTQ, R, S, T and XYZWXYZWX, Y, Z, W were congruent, so she tried to map one figure on
1 answer:
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Answer:
The correct option is;
∠A ≅ ∠X
Step-by-step explanation:
The given coordinates of the points of triangle ACB are;
A(-4, 4), C(-1, 3), B(-4, 0)
The given coordinates of the points of triangle XYZ are;
X(0, 8), Y(8, 8), Z(6, 2), therefore, we have
The length. l. of segment is given by the following formula;
For the length of the segment AC; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-1, 3), l = √(10)
For the length of the segment AB; (x₁, y₁) = (-4, 4), (x₂, y₂) = (-4, 0), l = 4
For the length of the segment BC; (x₁, y₁) = (-4, 0), (x₂, y₂) = (-1, 3), l = 3·√2
For the length of the segment XY; (x₁, y₁) = (0, 8), (x₂, y₂) = (8, 8), l = 8
For the length of the segment XZ; (x₁, y₁) = (0, 8), (x₂, y₂) = (6, 2), l = 6·√2
For the length of the segment ZY; (x₁, y₁) = (6, 2), (x₂, y₂) = (8, 8), l = 2·√(10
Therefore;
XY ~ AB, XZ ~ BC, ZY ~ AC
Which gives;
∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z
Answer:
Wendy jogs 13.75 mile in all each week
Step-by-step explanation:
To determine how many miles Wendy jogs in all each week,
we will sum the distance she jogs in the city with her running club in a week to the distance she jogs along the nature trail near her home in a week.
The distance she jugs with her running club = 5.5 mile.
Now, we will determine the distance of the nature trail near her home.
From the question, the nature trail is 1.5 times as long as the route in the city.
Let the distance of the nature trail =
and the distance of the route in the city be
Hence, we can write that
distance of the route in the city, = 5.5 mile
∴
8.25 miles
Hence, the nature trail is 8.25 mile
Then, the number of miles Wendy jogs in all each week is
5.5 mile + 8.25 mile = 13.75 mile
Hence, Wendy jogs 13.75 mile in all each week