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dolphi86 [110]
3 years ago
13

Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its b

ase is perpendicular to the base
Mathematics
1 answer:
Natalija [7]3 years ago
6 0

Answer:

Slope of the base segment line is zero, hence base segment is horizontal

Slope of the segment that joins the vertex angle to the midpoint of its base is undefined hence the line is vertical

Therefore, angle between base segment line and the segment line from the vertex angle to the midpoint is perpendicular

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base

Step-by-step explanation:

Here we prove the required relation as follows;

Let the isosceles be ABC

The coordinates of the points are

C = (0, 0) (Vertex)

A =  (-a, b)

C = (a, b)

P = (0, b) (Midpoint of base)

Therefore, the gradient or slope of the base AC is presented as follows;

Slope, m \, of \. base, \, AC= \frac{dy}{dx}  = \frac{b - b}{a - (-a)}  = \frac{0}{2\cdot a} = 0

Hence, segment AC is vertical

Slope, m \, of \, segment \ CP \,  joining \, vertex, \, to \, midpoint, P, on  \,AC = \frac{0 - b}{0 - 0}  = \frac{-b}{0} = Undifined.

Hence, segment CP is vertical

Therefore, the segment that joins the vertex angle to an isosceles triangle to the midpoint of its base is perpendicular to the base.

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What fraction is equivalent to 0.997
Katena32 [7]
It’s is 997/1000. Just put the number over the highest decimal place
8 0
3 years ago
Can someone help me please ASAP
zmey [24]

Answer:

<h2>140°</h2>

solution,

Let <DEF= x°

<CDE= 2x°

<BAF= 90°

The sum of interior angle of hexagon= 720°

<A + <B + <C + <D + <E +<F = 720°

90 + 145 + 115 + 2x + x + 160 = 720 \\ 510 + 3x = 720 \\3x + 510 = 720 \\ 3x + 510 - 510 = 720 - 510 \\ 3x = 210 \\  \frac{3x}{x}  =  \frac{210}{3}  \\ x = 70 \: degree

Again,

< \: cde = 2x \\  \:  \:  \:  \:  \:   \:  \:  \:  \:  \:  \:  \:  = 2 \times 70 \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  = 140 \: degree

Hope this helps...

Good luck on your assignment..

4 0
3 years ago
Lara bought 3 yards of fabric and a spool of thread for $28.10. If the spool of thread cost $1.25, how much did the fabric cost
Lyrx [107]

Answer: $8.95 per yard of fabric

Step-by-step explanation:

Define the following:

x = cost of fabric per yard

Make an equation:

⇒ 3x + 1.25 = 28.10

⇒ 3x = 26.85

⇒ x = 8.95

∴ $8.95 per yard of fabric

7 0
2 years ago
How much tax is withheld from 53,620 if tax rate is 7%.?
Tems11 [23]

The withheld tax is 3753.4

To get this you do 53,620 x .07

3 0
3 years ago
Read 2 more answers
BRAINLIEST ASAP! PLEASE HELP ME :)
Afina-wow [57]

Answer:

\large \boxed{\textbf{30.54 yr}}

Step-by-step explanation:

For species A,

P =2000e^{0.05t}

For species B,

P =5000e^{0.02t}

When their populations are equal,

\begin{array}{rcl}2000e^{0.05t} & = & 5000e^{0.02t}\\e^{0.05t} & = & 2.5e^{0.02t}\\0.05t & = & \ln2.5 + 0.02t\\0.05t & = & 0.9163 + 0.02t\\0.03t & = & 0.9163\\t& = & \dfrac{0.9163}{0.03}\\\\& = & \mathbf{30.54}\\\end{array}\\\text{The populations of species A and B will be the same in $\large \boxed{\textbf{30.54 yr}}$}

The diagram below shows the population of Species A overtaking that of Species B in about 30.5 yr.

3 0
3 years ago
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