Dissecting Triangles

According to the converse of the Perpendicular Bisector Theorem, if a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

In the diagram,

D

is equidistant from the endpoints of

\overline{T C} .

This and the fact that

D Y

and

\overline{T C}

are perpendicular, mean that

D Y

is the perpendicular bisector of

\overline{T C} .

Therefore, we can say that

T Y = Y C .

With this, we can write an equation to find

x .

T Y = Y C \Rightarrow 5 x = 3 x + 3

Let's subtract

3 x

on both sides to find the value of

x .

5 x = 3 x + 3

SubEqn

LHS - 3 x = RHS - 3 x

2 x = 3

DivEqn

LHS / 2 = RHS / 2

x = \frac{3}{2}

Finally, to find the value of

T Y,

we will substitute

\frac{3}{2}

for

x

in the expression

5 x .

T Y = 5 x

Substitute

x = \frac{3}{2}

T Y = 5 \cdot \frac{3}{2}

MoveLeftFacToNum

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

T Y = \frac{1 5}{2}

CalcQuotCalculate quotient

T Y = 7.5

Dissecting Triangles 1.2 - Solution