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# QLT1 Task 4, proving isosceles with bisector

Mathematics

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K
H J
FROM FIGURE PROVE THAT ∆HIJ IS Isosceles with bisector
I

Statements Reasons
Step 1
IKH=∠IKJ
Step 1
Given.
Step 2
KHJ=KJH
Step 2
In ∆HKJ, Opposite angles are equal as it is
Isosceles triangle.
Step 3
KH=KJ
Step 3
If opposite angles are equal in Isosceles
triangle then opposite sides are also
equal.
Step 4
KHJ =∠IHK +IHJ
Step 4
Sum of angles in given triangle.
Step 5
KJH =∠IJK+∠IJH
Step 5
Sum of angles in given triangle.
Step 6
IHJ=∠IJH
Step 6
Opposite Angles of Isosceles triangle are
equal.
Step 7
Then IH=IJ
Step 7
Opposite sides are also equal, If the
opposite angles are equal in an Isosceles
triangle.
Step 8
As IHJ=∠IJH And IH=IJ
Step 8
Then from these, It is concluded that ∆HIJ
is Isosceles.
Step 9 Step 9
Solution:
Note: The number of rows/steps provided in the proof table above is arbitrary and not
necessarily representative of the number of statements needed to complete this proof
logically.

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