The true and false statements need to be identified.
1. true
2. true
3. false
4. false
5. true
In an isosceles triangle two angles are equal.
Let the equal angle be [tex]x[/tex] and the other angle be [tex]y[/tex]
The sum of angles is [tex]180^{\circ}[/tex]
[tex]x+x+y=180\\\Rightarrow y=180-2x[/tex]
Now the value of [tex]x[/tex] cannot be [tex]90^{\circ}[/tex] or greater because
[tex]y=180-2\times 90=0[/tex]
[tex]x[/tex] has to be less than [tex]90^{\circ}[/tex].
The two equal angles must always be acute.
So, the statement is true.
If the side of an equilateral triangle is [tex]\dfrac{P}{3}[/tex]
Perimeter will be
[tex]\dfrac{P}{3}+\dfrac{P}{3}+\dfrac{P}{3}=P[/tex]
The statement is true.
An isosceles triangle that has the legs equal and also the base equal is called an equilateral triangle.
In an isosceles triangle the base may not be equal to the other two sides.
The statement is false.
Let [tex]x=1\ \text{unit}[/tex] be the length of the equal sides and [tex]y[/tex] the length of the other side
Permiter is
[tex]P=x+x+y\\\Rightarrow P=2x+y\\\Rightarrow P=2\times 1+y=2+y[/tex]
Since, the other side is not know the perimeter cannot be found.
The statement is false.
In an equilateral triangle all angles are [tex]60^{\circ}[/tex]
Exterior angle is found by subtracting the interior angle from [tex]180^{\circ}[/tex]
So, for an equilateral triangle the exterior angles will always be [tex]180-60=120^{\circ}[/tex]
The angles is greater than [tex]90^{\circ}[/tex] always.
The statement is true.
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