a. The length of the midsegment of an equilateral triangle is 6.25 cm
b. The length of AT is 33 units.
c. The value of y is 3.
What is an equilateral triangle?
"It is a triangle whose all sides are equal in length and all angles measure 60° "
What is perpendicular bisector?
"It is a line that intersects another line perpendicularly and divides it into wo equal parts."
What is angle bisector?
"It is a line that splits an angle into two equal angle."
What is an isosceles triangle?
"It is a triangle that has two sides of equal length."
What is midsegment of the triangle?
"It is the line segment connecting the midpoints of the two sides of a triangle."
What is midsegment formula?
"midsegment = 0.5 × base of triangle"
a.
We have been given an equilateral triangle with side lengths of 12.5 cm.
We need to find the length of the midsegment of an equilateral triangle.
Using midsegment formula,
⇒ midsegment = 0.5 × 12.5
⇒ midsegment = 6.25 cm
Therefore, the length of the midsegment of an equilateral triangle is 6.25 cm
b.
UT is the perpendicular bisector of line segment AB, where T is on AB
We know that the perpendicular bisector divides the line segment into two equal parts.
⇒ AT = TB
⇒ 3x + 6 = 42 - x
⇒ 3x + x = 42 - 6
⇒ 4x = 36
⇒ x = 9
So, the length of AT would be,
⇒ AT = 3x + 6
⇒ AT = 3(9) + 6
⇒ AT = 33 units
Therefore, the length of AT is 33 units.
c.
An angle EFG has angle bisector FH, where EF = GF
From given data, we can say that for it must an isosceles triangle EFG with EF = GF and base is EG.
An angle EFG has angle bisector FH and point H is on the side EG.
We know that the angle bisector of isosceles triangle is also the perpendicular bisector of the base of an isosceles triangle.
⇒ EH = HG
⇒ 5y + 10 = 28 - y
⇒ 5y + y = 28 - 10
⇒ 6y = 18
⇒ y = 3
Therefore, the value of y is 3.
Learn more about the angle bisector and perpendicular bisector here:
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