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stiv31 [10]
3 years ago
12

Which of the following is the Triangle Proportionality Theorem?

Mathematics
2 answers:
aivan3 [116]3 years ago
8 0
A a line parallel to one side of a triangle divides the other two sides
inna [77]3 years ago
3 0

Answer:

Option A is the correct answer

Step-by-step explanation:

We are required to determine which of the options represents the 'Triangle Proportionality Theorem'.

As, we know,

Triangle Proportionality Theorem states that,

<em>'If a line which is parallel to one side of a triangle intersects both the other two sides of the triangle, then it divides the other two sides into equal proportions'.</em>

So, according to the options, we get that,

A) A line parallel to one side of a triangle divides the other two sides proportionally

represents the Triangle Proportionality Theorem.

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Marta said 50 + one-half m = 120 is an equation, while Maribel argued that it is an expression. Determine who is correct and exp
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Answer:

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Step-by-step explanation:

We are given that

50+\frac{1}{2}m=120

We have to find who is correct and explain.

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Equation: It is mathematical sentence that combines  numbers and variables which shows the equality of two expressions.

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Question 14, Part (i)

Focus on quadrilateral ABCD. The interior angles add to 360 (this is true for any quadrilateral), so,

A+B+C+D = 360

A+90+C+90 = 360

A+C+180 = 360

A+C = 360-180

A+C = 180

Since angles A and C add to 180, this shows they are supplementary. This is the same as saying angles 2 and 3 are supplementary.

==================================================

Question 14, Part (ii)

Let

x = measure of angle 1

y = measure of angle 2

z = measure of angle 3

Back in part (i) above, we showed that y + z = 180

Note that angles 1 and 2 are adjacent to form a straight line, so we can say

x+y = 180

-------

We have the two equations x+y = 180 and y+z = 180 to form this system of equations

\begin{cases}x+y = 180\\y+z = 180\end{cases}

Which is really the same as this system

\begin{cases}x+y+0 = 180\\0+y+z = 180\end{cases}

The 0s help align the y terms up. Subtracting straight down leads to the equation x-z = 0 and we can solve to get x = z. Therefore showing that angle 1 and angle 3 are congruent. We could also use the substitution rule to end up with x = z as well.

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