What other information do you need to prove triangle INF=CAT by the ASA Postulate?
1 answer:
Label the angles on the given figure an x and y and label the unknown angles as z (see the figure below).
Because the sum of angles in a triangle = 180°, angle z is correct for all three triangles.
In order to prove that ΔINF = ΔCAT by the ASA Postulate,
1. We should show that AC = IN, or
2. We should show that AT = NF.
Proving either of the two options means that we have congruent isosceles triangles.
Because the sum of angles in a triangle = 180°, angle z is correct for all three triangles.
In order to prove that ΔINF = ΔCAT by the ASA Postulate,
1. We should show that AC = IN, or
2. We should show that AT = NF.
Proving either of the two options means that we have congruent isosceles triangles.
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It is given that two vertices of square are (0,0) and (4,2).
Now the problem is that you haven't given that whether these two vertices are adjacent vertices or opposite vertices of the square.
1. By Supposing that these two are adjacent vertices of Square
The third vertex will be at (-4,2) which lies in third quadrant.
Suppose the coordinate of fourth vertex be (x,y).
Mid point of line joining (4,2) and (-4,2) is{ [4+(-4)]/2,(2+2)/2} is (0,2).
Mid point of line joining (x,y) and (0,0) is (x/2,y/2).
Since diagonals of square bisect each other,
∵ x/2=0
⇒x=0
and
y/2=2
⇒y=4
So, The Coordinate of fourth vertex is (0,4).
Now coming back to second condition if these are two opposite vertex of Square.
Let the third coordinate be (a,b).
Length of diagonal=
Now,let side of Square be A.
Then length of Diagonal of square =√2 A
⇒√2 A=2√5
⇒A =√10
As third vertex is (a,b).
Using distance formula
a² + b²=10 -------------(1)
(a-4)²+ (b-2)²=10 --------------(2)
Solving expression (1) and (2), we get
⇒a²+ b²=(a-4)² +(b-2)²
⇒2a + b =5
⇒b=5-2a
Putting the value of b in (1),we get
⇒a² +(5-2a)²=10
⇒a²+25+4a²-20a =10
⇒5a²-20a+15=0
⇒a² - 4a + 3=0
Splitting the middle term,we get
⇒(a-3)(a-1)=0
⇒a=3 ∧ a=1
we get b=5-2×1=3 and b=5-2×3=5-6=-1
So,the other vertex are (1,3) and(3,-1).
Step-by-step explanation:
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